Curvature properties of some submanifolds in space forms
Abstract
Curvature properties of pseudosymmetry type of some submanifolds of codimension greater then 1 immersed isometrically in semi-Riemannian spaces of constant curvature are given.
References
K. Arslan, R. Deszcz, S. Yaprak, On Weyl-pseudosymmetric hypersurfaces, Colloq. Math. 72 (1997), 353-361.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Belkhelfa, R. Deszcz, M. G logowska, M. Hotloś, D. Kowalczyk, L. Verstraelen, A review on pseudosymmetry type manifolds, in: Banach Center Publ. 57, Inst. Math., Polish Acad. Sci., 2002, 179-194.
##plugins.generic.googleScholarLinks.settings.viewInGS##
E. Cartan, La déformation des hypersurfaces dans l’espace conforme réel à n ≥5 dimensions, Bull. Soc. Math. France 45 (1917), 57-121.
##plugins.generic.googleScholarLinks.settings.viewInGS##
T.E. Cecil, P.J. Ryan, Tight and Taut Immersions of Manifolds, Pitman Publishing Inc., Boston – London – Melbourne, 1985.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B.-Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B.-Y. Chen, L. Verstraelen, Codimension 2 submanifolds with a quasi-umbilical normal direction, J. Korean Math. Soc. 13 (1976), 87-97.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B.-Y. Chen, L. Verstraelen, A characterization of totally quasiumbilical submanifolds and its applications, Bull. Un. Mat. Ital. 14 (1977), 49-57. Errat. corrigé: ibid. 14 (1977), 634.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B.-Y. Chen, K. Yano, Sous-variétés localement conformes à un espace euclidien, C.R. Acad. Sc. Paris, Sér. A 275 (1972), 123-125.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B.-Y. Chen, K. Yano, Special quasi-umbilical hypersurfaces and locus of spheres, Atti Ac. Naz. Lincei 53 (1972), 255-260.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Deprez, R. Deszcz, L. Verstraelen, Pseudosymmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Toulouse 9 (1988), 183-192.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Deprez, R. Deszcz, L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Deprez, R. Deszcz, L. Verstraelen, S.. Yaprak, Hypersurfaces satisfying pseudosymmetry type conditions for their Weyl conformal curvature tensor, Atti Accad. Peloritana Pericolanti, Cl. Sci. Fis. Mat. Nat. 73 (1995), 165-181.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudosymmetry curvature conditions, in: Geometry and Topology of Submanifolds, II, World Sci., Teaneck, NJ, 1990, 134-143.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor N.S. 49 (1990), 134-145.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103- 120.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space, Results in Math. 20 (1991), 600-621.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Belg. Math., Ser. A, 44 (1992), 1-34.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifolds, Colloq. Math. 65 (1993), 139-147.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, Pseudosymmetric hypersurfaces in spaces of constant curvature, Tensor N.S. 58 (1997), 253-269.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, On certain classes of hypersurfaces in spaces of constant curvature, in: Geometry and Topology of Submanifolds, VIII, World Sci., River Edge, NJ, 1996, 101-110.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, L. Verstraelen, Hypersurfaces of semi-Riemannian conformally flat manifolds, in: Geometry and Topology of Submanifolds, III, World Sci., River Edge, NJ, 1991, 131-147.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, L. Verstraelen, S.. Yaprak, On 2-quasi-umbilical hypersurfaces in conformally flat spaces, Acta Math. Hungarica 78 (1998), 45-57.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, L. Verstraelen, S.. Yaprak, Hypersurfaces with pseudosymmetric Weyl tensor in conformally flat manifolds, in: Geometry and Topology of Submanifolds, IX, World Sci., 108-117.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, S.. Yaprak, Curvature properties of Cartan hypersurfaces, Colloq. Math. 67 (1994), 91-98.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Deszcz, S.. Yaprak, Curvature properties of certain pseudosymmetric manifolds, Publ. Math. Debrecen 45 (1994), 333-345.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G.M. Lancaster, Canonical metrics for certain conformally Euclidean spaces of dimension three and codimension one, Duke Math. J. 40 (1973), 1-8.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ü. Lumiste, M. Välijas, On geometry of totally quasiumbilical submanifolds, Tart. Univ. 836 (1989), 172-185.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J.D. Moore, J.M. Morvan, Sous-variétés conformément plates de codimension quatre, C.R. Acad. Sc. Paris, Sér. A, 287 (1978), 655-657.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J.M. Morvan, G. Zafindratafa, Conformally flat submanifolds, Ann. Fac. Sci. Toulouse 8 (1986-1987), 331-347.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Rosca, L. Verstraelen, On submanifolds admitting a normal section which is quasi-concircular w.r.t. a corresponding principal tangent section, Bull. Math. Soc. Sci. Math. R.S. Roumanie 20 (1976), 399-402.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J.A. Schouten, Über die konforme Abbildung n-dimensionaler Mannigfaltigkeiten mit quadratischen Massbestimmung auf eine Mannigfaltigkeit mit euklidischer Masssbestimmung, Math. Z. 11 (1921), 58-88.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Z.I. Szabó, Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0. I. The local version, J. Diff. Geom. 12 (1982), 531-582.
##plugins.generic.googleScholarLinks.settings.viewInGS##
L. Verstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, in: Geometry and Topology of Submanifolds, VI, World Sci., River Edge, NJ, 1994, 199-209.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Zafindratafa, Sous-varietes soumises a des conditions de courbure, Ph. D. Thesis, K.U. Leuven, Faculteit Wetenschappen, 1991.
##plugins.generic.googleScholarLinks.settings.viewInGS##