CURRICULUM VITAE ET STUDIORUM OF GIOVANNI CALVARUSO

NAME: Giovanni Francesco Calvaruso

PLACE AND DATE OF BIRTH:  Lecce (Italy), December 1971

ACADEMIC POSITION: Full  Professor  (University of Salento). Member of UMI, G.N.S.A.G.A.

Reviewer for Mathscinet and Zentralblatt.

CURRICULUM STUDIORUM:  DEGREE IN MATHEMATICS: University of Lecce, 28th of  April 1995, cum Laude. T.hesis: "Curvatura e caratteristica di Eulero-Poincaré". Supervisor: Prof.Domenico Perrone.

Winner of Prize “Young Hopes of Pugliese Culture”, organized by “Centro Artistico e Culturale “Renoir” di Taranto, as best graduated  in Mathematics from Puglia and Basilicata for the academic year 1993/94.

GRANTS AND STUDIES ABROAD:

•    C.N.R. grant for undergraduated, 1994-95 (Bando 209.01.60);

•    Grant for specialisation abroad, by University of Lecce (D.R. 1106), used for a two years stay (1996-1997) at the Kaholieke Universiteit Leven (Belgium), under the direction of Prof. L. Vanhecke;

•    Grant C.N.R., post-lauream, 1997.

PARTICIPATION TO NATIONAL RESEARCH PROJECTS:

PRIN on “Geometria delle varietà reali e complesse” (1998/99, 2000/01, 2002/03) (Research Unit directed by Prof. S.Marchiafava, Univ. “La Sapienza” di Roma).

PRIN on Differential Geometry (2006/2007, 2008/2009) (Research Unit directed by Prof. D. Perrone, Univ. del Salento).         

 National project "Progetto Lauree Scientifiche" (2006/2007, 2008/2009).

Local Director for Piano Nazionale Lauree Scientifiche" (from 2010/2011)

4.  CONFERENCES I attended:

I) As Main Speaker:

a. 10^th Panhellenic Conference, Patras (Grecia), May 2011.

b. Workshop on Lorentzian homogeneous spaces, Madrid (Spagna), March 2013

c. VII International Meeting on Lorentzian Geometry, Sao Paulo (Brasile), July 2013.

d. Varietà reali e complesse: geometria, topologia e analisi armonica, SNS Pisa, February 2014.

e. Geometric structures on Riemannian manifolds, Bari, 25-26 June 2015.

f. Varietà reali e complesse: geometria, topologia e analisi armonica, SNS Pisa, February 2017.

g. Geometric Analysis in Castro,  Castro, June 2022.

h. Symmetry and Shape, Santiago de Compostela (Spagna), 21-28 settembre 2024.

II) As Speaker:

 1. Workshop on Recent Topics in Differential Geometry, Santiago de Compostela (Spain), July 1997 [5].

 2. Nuovi Contributi Italiani alla Geometria Differenziale I, Bari, September 1997.

 3. Convegno G.N.S.A.G.A., Perugia, October 1998.

 4. Geometria delle Varietà Reali e Complesse. Nuovi Contributi Italiani II, Palermo, September 1999.

 5. IV International Workshop in Differential Geometry, Brasov (Romania), September 1999 [8].

 6. V International Workshop in Differential Geometry, Timisoara (Romania), September 2001 [13].

 7. Geometria delle Varietà Reali e Complesse. Nuovi Contributi Italiani III, Palermo, September 2002.

 8. International Conference “Curvature in Geometry”, in honour of Prof. L. Vanhecke, Lecce, June 2003.

 9. VI International Workshop in Differential Geometry, Cluj-Napoca (Romania), September 2003.

10. IX International Conference on Differential Geometry and its Applications, Praga (Rep. Ceca), September 2004.  

11. International Workshop in Geometry and Physics, Budapest, September  2005.

12. ICM (International Congress of Mathematicians), Madrid, August 2006 (short talk nella sezione di Geometria Differenziale).

13. Workshop on Lorentzian Geometry, Santiago de Compostela (Spagna), February 2007.

14. PADGE 2007 (Pure and Applied Differential Geometry), Bruxelles (Belgio), April 2007.

15. Recent Advances in Differential Geometry,  in honour of Prof. O. Kowalski, Lecce, June 2007.

16. V International Meeting on Lorentzian Geometry, Martina Franca, July 2009.

17. A harmonic map fest, Cagliari, September 2009.

18. XI International Conference on Differential Geometry and its Applications, Brno (Rep. Ceca), September 2010.

19. Convegno conclusivo PRIN, L'Aquila, September 2011

20. XIX Congresso UMI, Bologna, September 2011 (short talk nella sezione di Geometria).

21. PADGE 2012 (Pure and Applied Differential Geometry), Lovanio (Belgio), September 2012.

22. Complex Geometry and Lie groups, Torino, June 2014.

23. Workshop in memory of Sergio Console, Torino, February 2015.

24. XX Congresso U.M.I., Siena, September 2015 (short talk nella sezione di Geometria).

25. VIII International Meeting on Lorentzian Geometry, Malaga, September 2016.

III) As Member of the Scientific Committee:

-        First International Conference on Differential Geometry, Fès (Marocco), aprile 2016.

-        RieMain in Contact, Cagliari, settembre 2016.

-        D.D.Geo., Lecce, settembre 2019.

-        VII Workshop on Complex Geometry and Lie groups, Lecce, maggio 2023.

-        Second International Conference on Differential Geometry, Fès (Marocco), ottobre 2024.

PROCEEDINGS OF CONFERENCES:

 
[a]. G. Calvaruso e L. Vanhecke: Ball-homogeneous spaces, Public. Dep.to de Geometria y Topologia, Univ. Santiago de Compostela (Spain), Proceedings of the Workshop on “Recent Topics in Differential Geometry”, 89 (1998), 35-51.

[b]. G. Calvaruso: Homogeneity on contact metric three-manifolds, Proceedings of the IV International Workshop in Differential Geometry, Brasov (Romania) (1999), 18-25.

[c]. G. Calvaruso: Spectral rigidity of closed minimal submanifolds, An. Univ. Timisoara Ser. Mat.-Inform. 39 (2001), Special issue: Mathematics, Proceedings of the V International Workshop in Differential Geometry, Timisoara (Romania), 2001, 123-134.

[d]. G. Calvaruso: Conformally flat semi-symmetric spaces, In: D. Andrica and P.A. Blaga (Eds.), Recent advances in Geometry and Topology, Proceedings of the VI International Workshop in Differential Geometry, Cluj-Napoca (Romania), 2003, Cluj Univ. Press, 123-129.

[e]. G. Calvaruso: Symmetry conditions on conformally flat Riemannian manifolds, Differential geometry and its applications, 19–27, Matfyzpress, Prague, 2005.

[f]. G. Calvaruso and R.A. Marinosci, Homogeneous geodesics of three-dimensional Lorentzian Lie groups. XV International Workshop on Geometry and Physics, 252–259, Publ. R. Soc. Esp., R. Soc. Mat. Esp., Madrid, 2007.

[g]. G. Calvaruso e Z. Dusek, A n.g.o. space whose geodesics need a reparametrization, Geometry, integrability and quantization, 167–174, Softex, Sofia, 2008.

[h]. G. Calvaruso, On the geometry of $g$-natural contact metric structures on the unit tangent sphere bundle, Pure and applied differential geometry—PADGE 2007, 23–31, Ber. Math., Shaker Verlag, Aachen, 2007.

[i]. G. Calvaruso, Naturally Harmonic Vector Fields, Note di Matematica 28, suppl. n. 1, 2009, 101–124.

[j].G. Calvaruso, Constructing metrics with prescribed geometry, Harmonic maps and differential geometry, 177–185,Contemp. Math. 542, Amer. Math. Soc., Providence, RI, 2011.

[k]. G. Calvaruso, Contact Lorentzian manifolds, Differential geometry and its applications, 29 (2011), S41–S51.

[l]. G. Calvaruso, On the geometry of four-dimensional Lorentzian Lie groups, Pure and applied differential geometry—PADGE 2012, 46–54, Ber. Math., Shaker Verlag, Aachen, 2013.

[m].  G. Calvaruso and V. Martin-Molina, Recent advances in paracontact metric geometry, Int. J. Geom. Meth. Mod. Phys., 11 (2014), 1460038, 8 pp.

[n]. G. Calvaruso, A complete classification of four-dimensional paraKahler Lie algebras, Complex Manifolds, 2 (2015), 1-10.

[o]. G. Calvaruso, Harmonicity properties of paracontact metric manifolds, Rend. Semin. Mat. Univ. Politec. Torino, 73 (2015), 37-50.

[p]. G. Calvaruso, The prescribed curvature problem in low dimension, Geometry, algebra and applications: from mechanics to cryptography, Springer Proc. Math. Stat. 161, 37-48.

[q]. G. Calvaruso, Four-dimensional pseudo-Riemannian Lie groups, Rend. Semin. Mat. Univ. Politec. Torino, 74 (2016), 31-43.
 

 
Chairman of the Teaching Committee of Mathematics from November 2018 to November 2022.

 a. Thesis advisor. I have been advisor of several Master theses and theses in Mathematics..

b. ACTIVITIES RELATED TO PHD IN MATHEMATICS.

-) Supervisor of a PhD thesis: “Geometric structures over special classes of semi-Riemannian manifolds”, Dr. Amirhesam Zaeim, Payame-Noor University (Iran), 2012.

-) Supervisor of a PhD thesis: "Geometry of paracontact metric manifolds", Dr. Antonella Perrone, Università del Salento, 2015.

-) Supervisor (together with  Prof. S. Dragomir) of a PhD thesis: “Harmonic maps in Cauchy-Riemann Geometry”, Dr Francesco Esposito, dell’Università del Salento, 2021.

-) Member of Collegio dei Docenti del Dottorato in Matematica dell'Università del Salento, Ciclo XXVII.

-) International expert in the Committee for 2 PhD theses, at the University of Santiago de Compostela (Spain) and Universidad Complutense de Madrid (Spagna).

-) Teacher of the following PhD courses:

1. Algebra Lineare per il Dottorato (a.a. 2002/03, 2005/06).

2. Gruppi di Lie e algebre di Lie (a.a. 2011/12).

3. Introduzione alla Geometria pseudo-Riemanniana (a.a. 2013/14).

RESEARCH AREA: RIEMANNIAN AND PSEUDO-RIEMANNIAN GEOMETRY

My main research topics are listed below, in chronological order:

• BALL-HOMOGENEOUS SPACES
  

• CONTACT METRIC MANIFOLDS
  

• SPECTRAL GEOMETRY OF SUBMANIFOLDS
  

• HOMOGENEOUS GEODESICS IN HOMOGENEOUS SPACES
  

• SYMMETRY CONDITIONS ON RIEMANNIAN MANIFOLDS
  

• “$g$-NATURAL” METRICS ON THE UNIT TANGENT SPHERE BUNDLE

• HARMONICITY OF VECTOR FIELDS WITH RESPECT TO “$g$-NATURAL” METRICS
  

• HOMOGENEITY OF LORENTZIAN MANIFOLDS
  

• CONSTRUCTION OF METRICS WITH PRESCRIBED CURVATURE PROPERTIES.

• GEOMETRY OF SUBMANIFOLD
  

   PUBLICATIONS:
 

BOOK: G. Calvaruso and M. Castrillón López, Pseudo-Riemannian homogeneous structures. Developments in Mathematics, 59. Springer, Cham, 2019. xv+230 pp. ISBN: 978-3-030-18151-2; 978-3-030-18152-9.

PAPERS:

[1]. G. Calvaruso: Four-dimensional conformally flat Riemannian manifolds, Note di Matematica (2) 15 (1995), 153-159.

[2]. G. Calvaruso, Ph. Tondeur and L. Vanhecke: Four-dimensional ball-homogeneous and C-spaces, Beitrage Algebra Geom. (2) 38 (1997), 325-336.

[3]. G. Calvaruso and L. Vanhecke: Special ball-homogeneous spaces, Z. Anal. Anwendungen (4) 16 (1997), 789-800.

[4]. G. Calvaruso and L. Vanhecke: Semi-symmetric ball-homogeneous spaces and a volume conjecture, Bull. Austral. Math. Soc. (1) 57 (1998), 109-115.

[5]. G. Calvaruso, D. Perrone and L. Vanhecke: Homogeneity on three-dimensional contact metric manifolds, Israel J. Math. 114 (1999), 301-321.

[6]. G. Calvaruso and D. Perrone: Torsion and homogeneity on contact metric three-manifolds, Annali di Mat. Pura ed Appl. (4) 178 (2000), 271-285.

[7]. G. Calvaruso: Einstein-like and conformally flat contact metric three-manifolds, Balkan J. Geometry (2) 5 (2000), 17-36.

[8]. G. Calvaruso, R. A. Marinosci and D. Perrone: Three-dimensional curvature homogeneous hypersurfaces, Arch. Math. Brno (4) 36 (2000), 269-278.

[9]. G. Calvaruso and D. Perrone: Spectral geometry of the Jacobi operator of totally real submanifolds, Bull. Math. Soc. Roumanie, special number dedicated to the memory of Prof. G. Vranceanu, (3-4) 43 (93) (2000), 187-201.

[10]. G. Calvaruso and D. Perrone: On spectral geometry of minimal parallel submanifolds, Rend. Circolo Mat. Palermo Serie II 50 (2001), 103-116.

[11]. G. Calvaruso and D. Perrone: Semi-symmetric contact metric three-manifolds, Yokohama Mat. J. 49 (2002), 149-161.

[12]. G. Calvaruso: Totally real Einstein submanifolds of $CP^n$ and the spectrum of the Jacobi operator, Publ. Math. Debrecen (1-2) 64 (2002), 63-78.

[13]. G. Calvaruso: Spectral geometry of the Jacobi operator of totally real submanifolds of $QP^n$, Tokyo J. Math. (1) 28 (2005), 109-125.

[14]. G. Calvaruso and R. A. Marinosci: Homogeneous geodesics in five-dimensional generalized symmetric spaces,  Balkan J. Geom. (1) 8 (2002), 1-19.

[15]. G. Calvaruso, O. Kowalski and R. A. Marinosci, Homogeneous geodesics in solvable Lie groups, Acta Math. Hungarica (4) 101 (2003), 313-322.

[16]. E. Boeckx and G. Calvaruso, When is the unit tangent sphere bundle semi-symmetric?, Tohoku Math. J. (2) 56 (2004), 357-366.

[17]. G. Calvaruso, Conformally flat semi-symmetric spaces, Arch. Math. Brno 41 (2005), 27-36.

[18]. G. Calvaruso, Conformally flat pseudo-symmetric spaces of constant type, Czech. J. Math., 56 (131) (2006), 649-657.

[19]. G. Calvaruso, Contact metric geometry of the unit tangent sphere bundle, In: Complex, Contact and Symmetric manifolds, in Honour of L. Vanhecke, Progress in Math. 234 (2005), Birkhauser, Boston, Basel, Berlin, 41-57.

[20]. G. Calvaruso and D. Perrone, $H$-contact unit tangent sphere bundles, Rocky Mountain J.  Math., (5) 37 (2007), 1419-1442.

[21].  G. Calvaruso, Spectral geometry of totally complex submanifolds of $QP^n$, Kodai Math. J., (2) 29 (2006), 170-184.

[22]. M.T.K. Abbassi and G. Calvaruso, $g$-natural contact metrics on unit tangent sphere bundles, Monatsh. Math., 151 (2006),  89–109.

[23]. M.T.K. Abbassi and G. Calvaruso, The curvature tensor of $g$-natural metrics on unit tangent sphere bundles, Int. J. Contemp. Math. Sci., (6) 3 (2008), 245 – 258.

[24]. M.T.K. Abbassi and G. Calvaruso, Curvature properties of $g$-natural contact metric structures on unit tangent sphere bundles, Beitrage Algebra Geom., (1) 50 (2009), 155-178.

[25]. G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds, J. Geom. Phys., (4) 57 (2007), 1279-1291.

[26]. G. Calvaruso and R.A. Marinosci, Homogeneous geodesics of three-dimensional unimodular Lorentzian Lie groups, Mediterr. J. Math., (3-4) 3 (2006), 467-481.

[27]. G. Calvaruso and R.A. Marinosci, Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three, Adv. Geom. 8 (2008), 473–489.

[28]. G. Calvaruso, Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds, Geom. Dedicata, 127 (2007), 99-119.

[29]. M.T.K. Abbassi, G. Calvaruso and D. Perrone, Harmonic sections of tangent bundles equipped with $g$-natural Riemannian metrics, Quart. J. Math. 62 (2011), 259–288.

[30]. M.T.K. Abbassi, G. Calvaruso and D. Perrone, Harmonicity of unit vector fields with respect to Riemannian g-natural metrics, Diff. Geom. Appl. 27 (2009) 157–169.

[31]. G. Calvaruso, Pseudo-Riemannian $3$-manifolds with prescribed distinct constant Ricci eigenvalues, Diff. Geom. Appl. 26 (2008) 419–433.

[32]. M.T.K. Abbassi and G. Calvaruso, $g$-natural metrics of constant curvature on unit tangent sphere bundles, Arch. Math. (Brno), to appear.

[33]. G. Calvaruso, Einstein-like Lorentz metrics and three-dimensional curvature homogeneity of order one, Canadian Math. Bull., 53 (2010), 412–424.

[34]. G. Calvaruso, Einstein-like curvature homogeneous Lorentz three-manifolds, Res. Math., 55 (2009), 295–310.

[35]. G. Calvaruso, Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor, J. Math. Phys., 48 (2007),  123518, 1-17.

[36]. G. Calvaruso, Three-dimensional semi-symmetric homogeneous Lorentzian manifolds, Acta Math. Hung., 121 (1-2) (2008), 157-170.

[37]. G. Calvaruso and J. Van der Veken, Parallel surfaces in three-dimensional Lorentzian Lie groups, Taiwanese J. Math., 14 (2010), 223-250.

[38]. G. Calvaruso and J. Van der Veken, Lorentzian symmetric three-spaces and their parallel surfaces, Int. J. Math., 20 (2009), 1185-1205.

[39]. G. Calvaruso and O. Kowalski, On the Ricci operator of locally homogeneous Lorentzian $3$-manifolds, Central Eur. J. Math., (1) 7 (2009), 124-139.

[40]. G. Calvaruso and B. De Leo, On the curvature of four-dimensional generalized symmetric spaces, J. Geom., 90 (2008), 30-46.

[41]. G. Calvaruso, Nullity index of Bochner-K\"{a}hler manifolds, Note Mat., 29 (2008), 117-124.

[42]. M.T.K. Abbassi, G. Calvaruso and D. Perrone, Harmonic maps defined by the geodesic flow, Houston J. Math., 36 (2010), 69-90.

[43]. M.T.K. Abbassi, G. Calvaruso and D. Perrone, Examples of naturally harmonic sections, Ann. Math. Blaise Pascal, 55 (2009), 295–310.

[44]. G. Calvaruso, Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one, Abh. Sem. Amburgh, 79 (2009), 1-10.

[45]. W. Batat, G. Calvaruso and B. De Leo, Curvature properties of Lorentzian manifolds with large isometry groups, Mathematical Physics, Analysis and Geometry, 12 (2009), 201–217.

[46]. G. Calvaruso and B. De Leo, Semi-symmetric Lorentzian three-manifolds admitting a parallel degenerate line field,  Mediterr. J. Math., 7 (2010), 89–100.

[47]. G. Calvaruso, Curvature homogeneous Lorentzian three-manifolds,  Ann. Glob. Anal. Geom., 36 (2009) , 1-17.

[48]. W. Batat, G. Calvaruso and B. De Leo, Homogeneous structures on Lorentzian three-manifolds admitting a parallel null vector field, Balkan J. Geom. Appl., 14, (2009), 11-20.

[49]. G. Calvaruso, D. Kowalcyk and J. Van der Veken, On extrinsic simmetries of hypersurfaces of H^n x R, Bull. Austral. Math. Soc., 82 (2010), 390-400.

[50]. G. Calvaruso and J. Van der Veken, Parallel surfaces in three-dimensional reducible spaces, Proc. Roy. Soc. Edinburgh, to appear.

[51]. G. Calvaruso, Conformally flat Lorentzian three-spaces with different properties of symmetry and homogeneity, Arch. Math. (Brno), 46 (2010), 119–134.

[52]. G. Calvaruso and B. De Leo, Pseudo-symmetric Lorentzian three-manifolds, Int. J. Geom. Meth. Mod. Phys., (7) 6 (2009), 1–16.

[53]. W. Batat, G. Calvaruso and B. De Leo, On the geometry of four-dimensional Walker manifolds, Rend. Mat., 29 (2008), 163–173.

[54]. M.T.K. Abbassi and G. Calvaruso, Harmonic maps having tangent bundles with $g$-natural metrics as source or target, Rend. Sem. Mat. Torino, 68 (2010), 37–56.

[55]. G. Calvaruso, Three-dimensional Ivanov-Petrova manifolds, J. Math. Phys., 50 (2009)  063509, 1–12.

[56]. G. Calvaruso and J. Van der Veken, Parallel surfaces in Lorentzian three-manifolds admitting a parallel null vector field, J. Phys. A: Math. Theor. 43 (2010) 325207 (9pp).

[57]. G. Calvaruso, General Riemannian $3$-metrics with a Codazzi Ricci tensor, Geom. Dedicata, (1) 151 (2011), 259-267.  

[58]. G. Calvaruso and E. Garcia-Rio, Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups, SIGMA 6 (2010), 005, 1-8.

[59]. M. Brozos-Vazquez, G. Calvaruso, E. Garcia-Rio and S. Gavino-Fernandez, Three-dimensional Lorentzian homogeneous  Ricci solitons, Israel J. Math., 188 (2012), 385–403.

[60]. G. Calvaruso and D. Perrone, Homogeneous and  $H$-contact unit tangent sphere bundles, J. Austral. Math. Soc., 88 (2010), 323–337.

[61]. G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math.,55 (2011), 697–718.

[62]. G. Calvaruso and D. Perrone, Contact pseudo-metric manifolds, Diff. Geom. Appl., 28 (2010) 615–634.

[63]. G. Calvaruso and B. De Leo, Ricci solitons on three-dimensional Walker manifolds, Acta Math. Hung., 132 (3) (2011), 269–293.

[64]. G. Calvaruso and D. Perrone, Harmonic morphisms and Riemannian geometry of tangent bundles, Ann. Glob. Anal.  Geom., 39 (2010), 187-213.

[65]. G. Calvaruso, Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups, J. Geom. Phys., 61 (2011), 498–515.

[66]. G. Calvaruso and D. Perrone, Geometry of Kaluza–Klein metrics on the sphere S^3, Ann. Mat. Pura Appl., 192 (2013), 879–900.

[67]. G. Calvaruso and A. Fino, Five-dimensional $K$-contact Lie algebras, Monatsh. Math., 167 (2012), 35-59.

[68]. G. Calvaruso and A. Fino, Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces, Canadian J. Math., 64 (2012), 778–804.

[69]. G. Calvaruso, Three-dimensional paracontact Walker structures, Boll. U.M.I, Serie IX, 5 (2012), 387-403.

[70]. G. Calvaruso, Harmonicity of vector fields on four-dimensional generalized symmetric spaces, Central Eur. J. Math., 10 (2012), 411-425.

[71]. G. Calvaruso, Homogeneous contact metric structures on five-dimensional generalized symmetric spaces, Publ. Math. Debrecen, 81 (2012), 373-396.

[72]. G. Calvaruso and A. Fino, Complex and paracomplex structures on homogeneous pseudo-Riemannian four-manifolds, Int. J. Math. 24 (2013), 1250130, 1-28.

[73]. G. Calvaruso, Symplectic, complex and Kahler structures on four-dimensional generalized symmetric spaces, Diff. Geom. Appl., 29 (2011), 758–769.

[74]. G. Calvaruso and A. Fino, Four-dimensional pseudo-Riemannian homogeneous Ricci solitons, Int. J. Geom. Methods Mod. Phys.,  (5) 12  (2015), 1550056 (21 pp)

[75]. G. Calvaruso and A. Zaeim, Geometric structures over four-dimensional generalized symmetric spaces, Mediterr. J. Math., 10 (2013), 971–987.

[76]. G. Calvaruso and A. Zaeim, Four-dimensional homogeneous Lorentzian manifolds, Monatsh. Math., 174 (2014), 477-402.

[77]. G. Calvaruso, Four-dimensional paraKahler Lie algebras: classification and geometry, Houston J. Math., 41 (2015), 733-748.

[78]. G. Calvaruso and A. Zaeim, Geometric structures over non-reductive homogeneous 4-spaces, Adv. Geom., 14 (2014), 191-214.

[79]. G. Calvaruso and J. Van der Veken, Totally geodesic and parallel hypersurfaces of four-dimensional oscillator groups, Results Math., 64 (2013), 135–153.

[80]. G. Calvaruso and A. Zaeim, A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous $4$-spaces, J. Geom. Phys, 80 (2014), 15–25.

[81]. G. Calvaruso and D. Perrone, Metrics of Kaluza-Klein type on the anti-de Sitter space H_1^3, Math. Nachr., 287 (2014), 885-902.

[82]. G. Calvaruso and A. Zaeim, Conformally flat homogeneous pseudo-Riemannian four-manifolds, Tohoku Math. J., 66 (2014), 31-54.

[83]. G. Calvaruso, Three-dimensional homogeneous almost contact metric structures, J. Geom. Phys., 69 (2013), 60–73.

[84]. G. Calvaruso, A. Fino and A. Zaeim, Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian $4$-manifolds, Bull. Brazil. Math. Soc, 46 (2015), 1-42.

[85]. G. Calvaruso and D. Perrone, H-Contact semi-Riemannian manifolds, J. Geom. Phys., 71 (2013) 11–21.

[86]. G. Calvaruso and A. Zaeim, Four-dimensional Lorentzian Lie groups, Diff. Geom. Appl., 31 (2013) 496–509.

[87]. G. Calvaruso and A. Perrone, Left-invariant hypercontact structures on three-dimensional Lie groups, Period. Math. Hung., 69 (2014), 97-108.

[88]. G. Calvaruso and D. Perrone, Geometry of H-paracontact metric manifolds, Publ. Math. Debrecen, 86 (2015), 325–346.

[89]. G. Calvaruso and V. Martin-Molina, Paracontact metric structures on the unit tangent sphere bundle, Ann. Mat. Pura Appl., 194 (2015), 1359-1380.

[90]. G. Calvaruso and A. Perrone, Classification of 3D left-invariant almost paracontact metric structures, Adv. Geom., 17 (2017), 265-282.

[91]. G. Calvaruso and A. Zaeim, Left-invariant neutral metrics on four-dimensional Lie groups, J. Lie Theory, 25 (2015), 1023-1044.

[92]. G. Calvaruso and A. Perrone, Natural almost contact structures and their 3D homogeneous models, Math. Nachr., 289 (2016), 1370-1385.

[93]. G. Calvaruso and M.I. Munteanu, Hopf magnetic curves in the anti-de Sitter space $H_1^3$, J. Nonlin. Math. Phys., 25 (2018), 463-485.

[94]. G. Calvaruso and A. Zaeim, Invariant symmetries on non-reductive homogeneous pseudo-Riemannian four-manifolds,  Rev. Mat. Complut., 28 (2015), 599-622.

[95]. G. Calvaruso, M.I. Munteanu and A. Perrone, Killing magnetic curves in three-dimensional almost paracontact manifolds, J. Math. Anal. Appl., 426 (2015), 423-439.

[96]. G. Calvaruso and M. Castrillon-Lopez, Cyclic Lorentzian Lie groups, Geom. Dedicata, 181 (2016), 119-136.

[97]. G. Calvaruso and A. Perrone, Ricci solitons in three-dimensional paracontact geometry, J. Geom. Phys., 98 (2015), 1-12.  

[98]. G. Calvaruso and A. Zaeim, On the symmetries of the Lorentzian oscillator group, Collectanea Math., 68 (2017), 51-67 .

[99]. G. Calvaruso and A. Perrone, Five-dimensional paracontact Lie algebras, Diff. Geom. Appl., 45 (2016), 115–129.

[100]. G. Calvaruso, Oscillator spacetimes are Ricci solitons, Nonlinear Anal., 140 (2016), 254-269.

[101]. G. Calvaruso and A. Zaeim, Symmetries of Lorentzian three-manifolds with recurrent curvature, SIGMA Symmetry, integrability, Geometric Methods and Applications, 12 (2016), n. 63, 12pp.

[102]. G. Calvaruso and A. Perrone, Cosymplectic and \alpha-cosymplectic Lie algebras, Complex Manifolds 3 (2016), 252-270.

[103]. G. Calvaruso and E. Rosado, Ricci solitons on low-dimensional generalized symmetric spaces, J. Geom. Phys., 112 (2017), 106-117.

[104]. G. Calvaruso, Three-dimensional homogeneous generalized Ricci solitons, Mediterr. J. Math., 14 (2017), n. 216, 21pp.

[105]. G. Calvaruso and G. Ovando, From almost (para-)complex structures to affine structures on Lie groups, Manuscripta Math., 155 (2018), 89-113.

[106]. G. Calvaruso and A. Zaeim, Four-dimensional pseudo-Riemannian g.o. spaces and manifolds, J. Geom. Phys. , 130 (2018), 63-80.

[107]. M.T.K. Abbassi, N. Amri and G. Calvaruso , Kaluza-Klein type Ricci solitons on unit tangetn sphere bundles, Diff. Geom. Appl., 59 (2018), 184-203.

[108]. G. Calvaruso, The Ricci soliton equation and the structure of homogeneous Godel spacetimes, J. Math. Anal. Appl., 465 (2018), 1112-1133.

[109]. G. Calvaruso, Siklos spacetimes as homogeneous Ricci solitons, Class. Quantum Grav., 36 (2019), 095011 (13pp.).

[110]. G. Calvaruso, G. Metafune, L. Negro and C. Spina, Optimal kernel estimates for elliptic operators with second order discontinuous coefficients, J. Math. Anal. Appl., 485 (2020), 123763 (16pp.).

[111]. G. Calvaruso, R. Storm and J. Van der Veken, Parallel and totally geodesic hypersurfaces of non-reductive homogeneous four-manifolds, Math. Nachr. 293 (2020), 1707-1729.

[112]. G. Calvaruso, F. Esposito and D. Perrone, Levi flat CR-structures on 3D Lie algebras, Annali Mat. Pura Appl.,199 (2020), 2521-2542.

[113] M.T.K. Abbassi, N. Amri and G. Calvaruso, g-natural symmetries on tangent bundles, Math. Nachr., 293 (2020), 1873-1887.

[114]. G. Calvaruso and A. Zaeim, Homogeneous geodesics and natural reductivity of homogeneous Godel-type spacetimes, J.
Geom. Phys., 159(2021), 103919 (11pp.).

[115]. G. Calvaruso, On semi-direct extensions of the Heisenberg group, Collectanea Math., 72 (2021), 1-23.

[116]. A. Arvanitoyeorgos, G. Calvaruso and N. Souris, Two-step homogeneous geodesics in pseudo-Riemannian manifolds, Ann. Global Anal. Geom., 59 (2021), 297-317.

[117]. G. Calvaruso, Solutions of the Ricci soliton equation for a large class of Siklos spacetimes, Int. J. Geom. Methods Mod. Phys. 18 (2021), 2150052 (19 pp.).

[118]. G. Calvaruso, The Ricci soliton equation for homogeneous Siklos spacetimes, Note Mat. 41 (2021), 31–44.

[119]. G. Calvaruso and A. Zaeim, Conformal Geometry of semi-direct extensions of the Heisenberg group, J. Math. Phys. Anal. Geom., 17 (2021), no. 4, 407-421.

[120]. G. Calvaruso, M. Kaflou and A. Zaeim, On the symmetries of Siklos spacetimes, Gen. Relativity Gravitation 54 (2022), Paper No. 60, 26 pp.

[121]. G. Calvaruso and A. Zaeim, Critical metrics for quadratic curvature functionals on some solvmanifolds, Revista Mat. Complut. 36 (2023), 869-886.

[122]. G. Calvaruso, Einstein-like metrics on three-dimensional non-unimodular Lorentzian Lie groups, Bull. Iranian Math. Soc. 49 (2023), Paper No. 14, 14 pp.

[124]. G. Calvaruso, I. Onnis, L. Pellegrino and D. Uccheddu, Helix surfaces for Berger-like metrics on the anti-de Sitter space,Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. (RACSAM) 118 (2024), Paper No. 54.