# Curvature properties of certain compact pseudosymmetric manifolds

Colloquium Mathematicae (1993)

- Volume: 65, Issue: 1, page 139-147
- ISSN: 0010-1354

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topDeszcz, Ryszard. "Curvature properties of certain compact pseudosymmetric manifolds." Colloquium Mathematicae 65.1 (1993): 139-147. <http://eudml.org/doc/210197>.

@article{Deszcz1993,

author = {Deszcz, Ryszard},

journal = {Colloquium Mathematicae},

keywords = {pseudosymmetric Riemannian manifold; warped product},

language = {eng},

number = {1},

pages = {139-147},

title = {Curvature properties of certain compact pseudosymmetric manifolds},

url = {http://eudml.org/doc/210197},

volume = {65},

year = {1993},

}

TY - JOUR

AU - Deszcz, Ryszard

TI - Curvature properties of certain compact pseudosymmetric manifolds

JO - Colloquium Mathematicae

PY - 1993

VL - 65

IS - 1

SP - 139

EP - 147

LA - eng

KW - pseudosymmetric Riemannian manifold; warped product

UR - http://eudml.org/doc/210197

ER -

## References

top- [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] A. L. Besse, Einstein Manifolds, Springer, Berlin 1987. Zbl0613.53001
- [3] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. Zbl0191.52002
- [4] 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.
- [5] F. Defever and R. Deszcz, A note on geodesic mappings of pseudosymmetric Riemannian manifolds, Colloq. Math. 62 (1991), 313-319. Zbl0810.53008
- [6] F. Defever and R. Deszcz, On warped product manifolds satisfying a certain curvature condition, Atti Acad. Peloritana Cl. Sci. Fis. Mat. Natur., in print. Zbl0780.53017
- [7] F. Defever and R. Deszcz, On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor, Acta Univ. Palackiensis, in print. Zbl0796.53016
- [8] 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
- [9] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. Zbl0678.53022
- [10] R. Deszcz, Notes on totally umbilical submanifolds, in: Geometry and Topology of Submanifolds, Luminy, May 1987, World Sci., Singapore 1989, 89-97. Zbl0735.53042
- [11] R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudosymmetry curvature conditions, in: Geometry and Topology of Submanifolds, II, Avignon, May 1988, World Sci., Singapore 1990, 134-143.
- [12] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. Zbl0742.53006
- [13] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. Zbl0738.53008
- [14] R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space, Results in Math. 20 (1991), 600-621. Zbl0752.53009
- [15] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. Zbl0633.53031
- [16] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. Zbl0698.53011
- [17] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. Zbl0707.53019
- [18] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262. Zbl0668.53007
- [19] 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.
- [20] R. Deszcz, L. Verstraelen and L. Vrancken, On the symmetry of warped product spacetimes, Gen. Rel. Grav. 23 (1991), 671-681. Zbl0723.53009
- [21] G. I. Kruchkovich, On semi-reducible Riemannian spaces, Dokl. Akad. Nauk SSSR 115 (1957), 862-865 (in Russian). Zbl0080.37301
- [22] J. Mikesh, Geodesic mappings of special Riemannian spaces, in: Topics in Differential Geometry (Hajdoszoboszló 1984), Colloq. Math. Soc. János Bolyai 46, Vol. II, North-Holland, Amsterdam 1988, 793-813.
- [23] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333-340. Zbl0115.39302
- [24] 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

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