Curvature properties of Cartan hypersurfaces
Deszcz, Ryszard ; Yaprak, Sahnur
Colloquium Mathematicae, Tome 67 (1994), p. 91-98 / Harvested from The Polish Digital Mathematics Library
Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:210266
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     author = {Ryszard Deszcz and Sahnur Yaprak},
     title = {Curvature properties of Cartan hypersurfaces},
     journal = {Colloquium Mathematicae},
     volume = {67},
     year = {1994},
     pages = {91-98},
     zbl = {0816.53032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p91bwm}
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Deszcz, Ryszard; Yaprak, Sahnur. Curvature properties of Cartan hypersurfaces. Colloquium Mathematicae, Tome 67 (1994) pp. 91-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p91bwm/

[000] [1] A. Adamów and R. Deszcz, On totally umbilical submanifolds of some class of Riemannian manifolds, Demonstratio Math. 16 (1983), 39-59. | Zbl 0534.53019

[001] [2] E. Cartan, Familles de surfaces isoparamétriques dans les espaces à courbure constante, Ann. Mat. Pura Appl. 17 (1938), 177-191. | Zbl 64.1361.02

[002] [3] E. Cartan, Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335-367. | Zbl 0021.15603

[003] [4] T. E. Cecil and P. J. Ryan, Tight and Taut Immersions of Manifolds, Pitman, Boston, 1985. | Zbl 0596.53002

[004] [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.

[005] [6] F. Defever and R. Deszcz, A note on geodesic mappings of pseudosymmetric Riemannian manifolds, Colloq. Math. 62 (1991), 313-319. | Zbl 0810.53008

[006] [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. | Zbl 0780.53017

[007] [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. | Zbl 0796.53016

[008] [9] F. Defever, R. Deszcz and M. Prvanović, On warped product manifolds satisfying some curvature condition of pseudosymmetry type, to appear. | Zbl 0923.53018

[009] [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. | Zbl 0839.53039

[010] [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. | Zbl 0668.53010

[011] [12] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. | Zbl 0678.53022

[012] [13] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. | Zbl 0707.53020

[013] [14] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. | Zbl 0742.53006

[014] [15] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. | Zbl 0738.53008

[015] [16] R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, ibid. 65 (1993), 139-147. | Zbl 0823.53030

[016] [17] R. Deszcz, Pseudosymmetric hypersurfaces in manifolds of constant curvature, to appear. | Zbl 0938.53024

[017] [18] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), 1-34. | Zbl 0808.53012

[018] [19] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. | Zbl 0633.53031

[019] [20] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, Colloq. Math. 58 (1990), 259-268. | Zbl 0707.53019

[020] [21] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262. | Zbl 0668.53007

[021] [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. | Zbl 0744.53008

[022] [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.

[023] [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. | Zbl 0817.53008

[024] [25] R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica, in print. | Zbl 0811.53014

[025] [26] T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145-173. | Zbl 0196.25102

[026] [27] F. Tricerri and L. Vanhecke, Cartan hypersurfaces and reflections, Nihonkai Math. J. 1 (1990), 203-208. | Zbl 0956.53505

[027] [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. | Zbl 0508.53025