On the equivalence of Ricci-semisymmetry and semisymmetry
Arslan, Kadri ; Çelik, Yunus ; Deszcz, Ryszard ; Ezentaş, Ridvan
Colloquium Mathematicae, Tome 78 (1998), p. 279-294 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:210566
@article{bwmeta1.element.bwnjournal-article-cmv76z2p279bwm,
     author = {Kadri Arslan and Yunus \c Celik and Ryszard Deszcz and Ridvan Ezenta\c s},
     title = {On the equivalence of Ricci-semisymmetry and semisymmetry},
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {279-294},
     zbl = {0901.53010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p279bwm}
}
Arslan, Kadri; Çelik, Yunus; Deszcz, Ryszard; Ezentaş, Ridvan. On the equivalence of Ricci-semisymmetry and semisymmetry. Colloquium Mathematicae, Tome 78 (1998) pp. 279-294. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p279bwm/

[000] [1] E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Sci., Singapore, 1996. | Zbl 0904.53006

[001] [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. | Zbl 0832.53015

[002] [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. | Zbl 0952.53013

[003] [4] F. Defever, R. Deszcz and L. Verstraelen, On semisymmetric para-Kähler manifolds, Acta Math. Hungar. 74 (1997), 7-17. | Zbl 0922.53009

[004] [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. | Zbl 1038.53020

[005] [6] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. | Zbl 0678.53022

[006] [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. | Zbl 0886.53005

[007] [8] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. | Zbl 0707.53020

[008] [9] R. Deszcz, On conformally flat Riemannian manifold satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. | Zbl 0742.53006

[009] [10] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. | Zbl 0738.53008

[010] [11] R. Deszcz, On pseudosymmetric spaces, Bull. Belg. Math. Soc. Ser. A 44 (1992), 1-34. | Zbl 0808.53012

[011] [12] R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, Colloq. Math. 65 (1993), 139-147. | Zbl 0823.53030

[012] [13] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322. | Zbl 0633.53031

[013] [14] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. | Zbl 0698.53011

[014] [15] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. | Zbl 0707.53019

[015] [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. | Zbl 0744.53008

[016] [17] R. Deszcz and M. Hotloś, On a certain subclass of pseudosymmetric manifolds, Publ. Math. Debrecen, in print. | Zbl 0907.53013

[017] [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.

[018] [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. | Zbl 0811.53014

[019] [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. | Zbl 0936.53038

[020] [21] R. Deszcz, L. Verstraelen and Ş. Yaprak, On 2-quasi-umbilical hypersurfaces in conformally flat spaces, Acta Math. Hungar. 78 (1998), 45-57. | Zbl 0905.53012

[021] [22] R. Deszcz and Ş. Yaprak, Curvature properties of Cartan hypersurfaces, Colloq. Math. 67 (1994), 91-98. | Zbl 0816.53032

[022] [23] R. Deszcz and Ş. Yaprak, Curvature properties of certain pseudosymmetric manifolds, Publ. Math. Debrecen 45 (1994), 333-345. | Zbl 0827.53031

[023] [24] Y. Matsuyama, Complete hypersurfaces with R·S = 0 in En+1, Proc. Amer. Math. Soc. 88 (1983), 119-123.

[024] [25] E. M. Patterson, A class of critical Riemannian metrics, J. London Math. Soc. 23 (1981), 349-358. | Zbl 0417.53025

[025] [26] P. J. Ryan, Hypersurfaces with parallel Ricci tensor, Osaka J. Math. 8 (1971), 251-259. | Zbl 0222.53025

[026] [27] P. J. Ryan, A class of complex hypersurfaces, Colloq. Math. 26 (1972), 175-182. | Zbl 0243.53028

[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

[028] [29] S. Tanno, Hypersurfaces satisfying a certain condition on the Ricci tensor, Tôhoku Math. J. 21 (1969), 297-303. | Zbl 0189.22403

[029] [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. | Zbl 0846.53034