@article{bwmeta1.element.bwnjournal-article-cmv62i1p103bwm,
author = {Ryszard Deszcz},
title = {On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions},
journal = {Colloquium Mathematicae},
volume = {62},
year = {1991},
pages = {103-120},
zbl = {0738.53008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv62i1p103bwm}
}
Deszcz, Ryszard. On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions. Colloquium Mathematicae, Tome 62 (1991) pp. 103-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv62i1p103bwm/
[000] [1] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. | Zbl 0191.52002
[001] [2] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. | Zbl 0678.53022
[002] [3] J. Deprez, R. Deszcz and L. Verstraelen, Pseudo-symmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Univ. Paul Sabatier Toulouse 9 (1988), 183-192. | Zbl 0668.53010
[003] [4] J. Deprez, P. Verheyen and L. Verstraelen, Characterization of conformally flat hypersurfaces, Czechoslovak Math. J. 35 (110) (1985), 140-145. | Zbl 0586.53001
[004] [5] A. Derdziński, Exemples de métriques de Kaehler et d'Einstein autoduales sur le plan complexe, in: Géométrie riemannienne en dimension 4 (Séminaire Arthur Besse 1978/79), Cedic/Fernand Nathan, Paris 1981, 334-346. | Zbl 0477.53025
[005] [6] R. Deszcz, On pseudo-symmetric warped product manifolds, to appear. | Zbl 0843.53011
[006] [7] R. Deszcz, On Ricci-pseudo-symmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. | Zbl 0707.53020
[007] [8] R. Deszcz, On pseudo-symmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zeszyty Naukowe Politech. Śląsk., in print. | Zbl 0418.53023
[008] [9] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.), in print. | Zbl 0742.53006
[009] [10] R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudo-symmetry curvature conditions, in: Geometry and Topology of Submanifolds, II, Avignon, May 1988, World Sci. Publ., Singapore 1990, 134-143.
[010] [11] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. | Zbl 0633.53031
[011] [12] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. | Zbl 0698.53011
[012] [13] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. | Zbl 0707.53019
[013] [14] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying certain curvature condition imposed on the Ricci tensor, Prace Nauk. Politech. Szczec. 11 (1989), 23-34. | Zbl 0744.53008
[014] [15] L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press, Princeton 1966.
[015] [16] W. Grycak, Riemannian manifolds with a symmetry condition imposed on the -nd derivative of the conformal curvature tensor, Tensor (N.S.) 46 (1987), 287-290. | Zbl 0694.53017
[016] [17] G. I. Kruchkovich, On semi-reducible Riemannian spaces, Dokl. Akad. Nauk SSSR 115 (1957), 862-865 (in Russian). | Zbl 0080.37301
[017] [18] K. Nomizu, On the decomposition of generalized curvature tensor fields, in: Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972, 335-345.
[018] [19] Y. Ogawa, On conformally flat spaces with warped product Riemannian metric, Nat. Sci. Rep. Ochanomizu Univ. 29 (1978), 117-127. | Zbl 0423.53010
[019] [20] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying , J. Differential Geom. 17 (1982), 531-582.