Curvature properties of Cartan hypersurfaces

 Access to full text

 Full (PDF)

1. [1] A. Adamów and R. Deszcz, On totally umbilical submanifolds of some class of Riemannian manifolds, Demonstratio Math. 16 (1983), 39-59. Zbl0534.53019
2. [2] E. Cartan, Familles de surfaces isoparamétriques dans les espaces à courbure constante, Ann. Mat. Pura Appl. 17 (1938), 177-191. Zbl64.1361.02
3. [3] E. Cartan, Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335-367. Zbl0021.15603
4. [4] T. E. Cecil and P. J. Ryan, Tight and Taut Immersions of Manifolds, Pitman, Boston, 1985. Zbl0596.53002
5. [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. [6] F. Defever and R. Deszcz, A note on geodesic mappings of pseudosymmetric Riemannian manifolds, Colloq. Math. 62 (1991), 313-319. Zbl0810.53008
7. [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. Zbl0780.53017
8. [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. Zbl0796.53016
9. [9] F. Defever, R. Deszcz and M. Prvanović, On warped product manifolds satisfying some curvature condition of pseudosymmetry type, to appear. Zbl0923.53018
10. [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. Zbl0839.53039
11. [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. Zbl0668.53010
12. [12] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. Zbl0678.53022
13. [13] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. Zbl0707.53020
14. [14] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. Zbl0742.53006
15. [15] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. Zbl0738.53008
16. [16] R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, ibid. 65 (1993), 139-147. Zbl0823.53030
17. [17] R. Deszcz, Pseudosymmetric hypersurfaces in manifolds of constant curvature, to appear. Zbl0938.53024
18. [18] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), 1-34. Zbl0808.53012
19. [19] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. Zbl0633.53031
20. [20] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, Colloq. Math. 58 (1990), 259-268. Zbl0707.53019
21. [21] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262. Zbl0668.53007
22. [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. Zbl0744.53008
23. [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. [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. Zbl0817.53008
25. [25] R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica, in print. Zbl0811.53014
26. [26] T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145-173. Zbl0196.25102
27. [27] F. Tricerri and L. Vanhecke, Cartan hypersurfaces and reflections, Nihonkai Math. J. 1 (1990), 203-208. Zbl0956.53505
28. [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. Zbl0508.53025

1. Miroslava Petrović-Torgašev, Leopold C. A. Verstraelen, On Deszcz symmetries of Wintgen ideal submanifolds
2. Kadri Arslan, Yunus Çelik, Ryszard Deszcz, Ridvan Ezentaş, On the equivalence of Ricci-semisymmetry and semisymmetry
3. Ryszard Deszcz, Marian Hotloś, Zerrin Şentürk, On the equivalence of the Ricci-pseudosymmetry and pseudosymmetry
4. Kadri Arslan, Ryszard Deszcz, Şahnur Yaprak, On Weyl pseudosymmetric hypersurfaces