On the equivalence of Ricci-semisymmetry and semisymmetry

 Access to full text

 Full (PDF)

1. [1] E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Sci., Singapore, 1996. Zbl0904.53006
2. [2] F. Defever, R. Deszcz, P. Dhooghe, L. Verstraelen and Ş. Yaprak, On Ricci-pseudosymmetric hypersurfaces in spaces of constant curvature, Results Math. 27 (1995), 227-236. Zbl0832.53015
3. [3] F. Defever, R. Deszcz, Z. Şentürk, L. Verstraelen and Ş. Yaprak, P. J. Ryan's problem in semi-Riemannian space forms, Dept. Math., Agricultural Univ. Wrocław, preprint No. 44, 1997. Zbl0952.53013
4. [4] F. Defever, R. Deszcz and L. Verstraelen, On semisymmetric para-Kähler manifolds, Acta Math. Hungar. 74 (1997), 7-17. Zbl0922.53009
5. [5] F. Defever, R. Deszcz, L. Verstraelen and Ş. Yaprak, The equivalence of semisymmetry and Ricci-semisymmetry for certain hypersurfaces, Dept. Math., Agricultural Univ. Wrocław, preprint No. 45, 1997. Zbl1038.53020
6. [6] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. Zbl0678.53022
7. [7] J. Deprez, R. Deszcz, L. Verstraelen and Ş. Yaprak, Hypersurfaces satisfying pseudosymmetry type conditions for their Weyl conformal curvature tensor, Atti Acad. Peloritana Cl. Sci. Fis. Mat. Natur., in print. Zbl0886.53005
8. [8] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. Zbl0707.53020
9. [9] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. Zbl0742.53006
10. [10] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. Zbl0738.53008
11. [11] R. Deszcz, On pseudosymmetric spaces, Bull. Belg. Math. Soc. Ser. A 44 (1992), 1-34. Zbl0808.53012
12. [12] R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, Colloq. Math. 65 (1993), 139-147. Zbl0823.53030
13. [13] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. Zbl0633.53031
14. [14] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. Zbl0698.53011
15. [15] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. Zbl0707.53019
16. [16] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying certain curvature condition imposed on the Ricci tensor, Prace Nauk. Politech. Szczec. 11 (1988), 23-34. Zbl0744.53008
17. [17] R. Deszcz and M. Hotloś, On a certain subclass of pseudosymmetric manifolds, Publ. Math. Debrecen, in print. Zbl0907.53013
18. [18] R. Deszcz and L. Verstraelen, Hypersurfaces of semi-Riemannian conformally flat manifolds, in: Geometry and Topology of Submanifolds, III, World Scientific, River Edge, N.J., 1991, 131-147. 
19. [19] R. Deszcz, L. Verstraelen and Ş. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica 22 (1994), 167-179. Zbl0811.53014
20. [20] R. Deszcz, L. Verstraelen and Ş. Yaprak, Hypersurfaces with pseudosymmetric Weyl tensor in conformally flat manifolds, Dept. Math., Agricultural Univ. Wrocław, preprint No. 32, 1995. Zbl0936.53038
21. [21] R. Deszcz, L. Verstraelen and Ş. Yaprak, On 2-quasi-umbilical hypersurfaces in conformally flat spaces, Acta Math. Hungar. 78 (1998), 45-57. Zbl0905.53012
22. [22] R. Deszcz and Ş. Yaprak, Curvature properties of Cartan hypersurfaces, Colloq. Math. 67 (1994), 91-98. Zbl0816.53032
23. [23] R. Deszcz and Ş. Yaprak, Curvature properties of certain pseudosymmetric manifolds, Publ. Math. Debrecen 45 (1994), 333-345. Zbl0827.53031
24. [24] Y. Matsuyama, Complete hypersurfaces with R·S = 0 in $E^n+1$, Proc. Amer. Math. Soc. 88 (1983), 119-123. 
25. [25] E. M. Patterson, A class of critical Riemannian metrics, J. London Math. Soc. 23 (1981), 349-358. Zbl0417.53025
26. [26] P. J. Ryan, Hypersurfaces with parallel Ricci tensor, Osaka J. Math. 8 (1971), 251-259. Zbl0222.53025
27. [27] P. J. Ryan, A class of complex hypersurfaces, Colloq. Math. 26 (1972), 175-182. Zbl0243.53028
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
29. [29] S. Tanno, Hypersurfaces satisfying a certain condition on the Ricci tensor, Tôhoku Math. J. 21 (1969), 297-303. Zbl0189.22403
30. [30] L. Verstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, in: Geometry and Topology of Submanifolds, VI, World Scientific, River Edge, N.J., 1994, 199-209. Zbl0846.53034

1. Ryszard Deszcz, Marian Hotloś, Zerrin Şentürk, On the equivalence of the Ricci-pseudosymmetry and pseudosymmetry