Curvature properties of Cartan hypersurfaces

• Autorzy: Ryszard Deszcz , Sahnur Yaprak
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1994
• Tom: 67
• Numer: 1
• Strony: 91-98

Daty

wydano

1994

otrzymano

1993-05-31

poprawiono

1993-10-08

Twórcy

autor

Ryszard Deszcz

• Department of Mathematics, Agricultural University of Wrocław, Norwida 25, 50-375 Wrocław, Poland

autor

Sahnur Yaprak

• Department of Mathematics, The University of Ankara, The Faculty of Science, 06100 Tandoḡan Ankara, Turkey

Bibliografia

• [1] A. Adamów and R. Deszcz, On totally umbilical submanifolds of some class of Riemannian manifolds, Demonstratio Math. 16 (1983), 39-59.
• [2] E. Cartan, Familles de surfaces isoparamétriques dans les espaces à courbure constante, Ann. Mat. Pura Appl. 17 (1938), 177-191.
• [3] E. Cartan, Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335-367.
• [4] T. E. Cecil and P. J. Ryan, Tight and Taut Immersions of Manifolds, Pitman, Boston, 1985.
• [5] F. Defever and R. Deszcz, On semi-Riemannian manifolds satisfying the condition R · R = Q(S,R), in: Geometry and Topology of Submanifolds, III, Leeds, May 1990, World Sci., Singapore, 1991, 108-130.
• [6] F. Defever and R. Deszcz, A note on geodesic mappings of pseudosymmetric Riemannian manifolds, Colloq. Math. 62 (1991), 313-319.
• [7] F. Defever and R. Deszcz, On warped product manifolds satisfying a certain curvature condition, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 69 (1991), 213-236.
• [8] F. Defever and R. Deszcz, On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor, Acta Univ. Palack., in print.
• [9] F. Defever, R. Deszcz and M. Prvanović, On warped product manifolds satisfying some curvature condition of pseudosymmetry type, to appear.
• [10] F. Defever, R. Deszcz, L. Verstraelen and S. Yaprak, Curvature properties of hypersurfaces of pseudosymmetry type, in: Geometry and Topology of Submanifolds, V, Leuven/Brussels, July 1992, World Sci., Singapore, 1993, 132-146.
• [11] J. Deprez, R. Deszcz and L. Verstraelen, Pseudosymmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Toulouse 9 (1988), 183-192.
• [12] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65.
• [13] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065.
• [14] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145.
• [15] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120.
• [16] R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, ibid. 65 (1993), 139-147.
• [17] R. Deszcz, Pseudosymmetric hypersurfaces in manifolds of constant curvature, to appear.
• [18] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), 1-34.
• [19] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322.
• [20] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, Colloq. Math. 58 (1990), 259-268.
• [21] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262.
• [22] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying a certain curvature condition imposed on the Ricci tensor, Prace Nauk. Polit. Szczec. 11 (1989), 23-34.
• [23] R. Deszcz and L. Verstraelen, Hypersurfaces of semi-Riemannian conformally flat manifolds, in: Geometry and Topology of Submanifolds, III, Leeds, May 1990, World Sci., Singapore, 1991, 131-147.
• [24] R. Deszcz, L. Verstraelen and S. Yaprak, Warped products realizing a certain condition of pseudosymmetry type imposed on the Weyl curvature tensor, Chinese J. Math., in print.
• [25] R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica, in print.
• [26] T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145-173.
• [27] F. Tricerri and L. Vanhecke, Cartan hypersurfaces and reflections, Nihonkai Math. J. 1 (1990), 203-208.
• [28] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying R(X,Y)·R = 0. I. The local version, J. Differential Geom., 17 (1982), 531-582.