PUBLICATIONS:
BOOK:
G. Calvaruso and M. Castrillon-Lopez, Pseudo-Riemannian homogeneous structures, Developments in Math., 59, Springer, Cham, 2019, xv+230pp. 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.
[123]. M.T.K. Abbassi, K. Boulagouaz and G. Calvaruso, On the Geometry of the Null Tangent Bundle of a Pseudo-Riemannian Manifold,Axioms 12 (2023), Paper No. 903, 55pp.
[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.
[125].
G. Calvaruso, L. Pellegrino and J. Van der Veken, Totally geodesic and
parallel hypersurfaces of Gödel-type spacetimes J. Geom. Phys. 198
(2024), Paper No. 105108.
PROCEEDINGS OF CONFERENCES: