On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions

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1. [1] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. Zbl0191.52002
2. [2] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. Zbl0678.53022
3. [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. Zbl0668.53010
4. [4] J. Deprez, P. Verheyen and L. Verstraelen, Characterization of conformally flat hypersurfaces, Czechoslovak Math. J. 35 (110) (1985), 140-145. Zbl0586.53001
5. [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. Zbl0477.53025
6. [6] R. Deszcz, On pseudo-symmetric warped product manifolds, to appear. Zbl0843.53011
7. [7] R. Deszcz, On Ricci-pseudo-symmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. Zbl0707.53020
8. [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. Zbl0418.53023
9. [9] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.), in print. Zbl0742.53006
10. [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. 
11. [11] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. Zbl0633.53031
12. [12] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. Zbl0698.53011
13. [13] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. Zbl0707.53019
14. [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. Zbl0744.53008
15. [15] L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press, Princeton 1966. 
16. [16] W. Grycak, Riemannian manifolds with a symmetry condition imposed on the $2$-nd derivative of the conformal curvature tensor, Tensor (N.S.) 46 (1987), 287-290. Zbl0694.53017
17. [17] G. I. Kruchkovich, On semi-reducible Riemannian spaces, Dokl. Akad. Nauk SSSR 115 (1957), 862-865 (in Russian). Zbl0080.37301
18. [18] K. Nomizu, On the decomposition of generalized curvature tensor fields, in: Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972, 335-345. 
19. [19] Y. Ogawa, On conformally flat spaces with warped product Riemannian metric, Nat. Sci. Rep. Ochanomizu Univ. 29 (1978), 117-127. Zbl0423.53010
20. [20] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying $R(X,Y)·R=0$, J. Differential Geom. 17 (1982), 531-582. 

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