On some family of generalized Einstein metric conditions

• Autorzy: Deszcz, R. , Hotloś, M. , Senturk, Z.
• Języki publikacji: EN

Abstrakty

EN

We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.

Słowa kluczowe

EN

Einstein manifold; pseudosymmetry type manifold

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 943-954
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Deszcz, R.

• Department of Mathematics Agricultural University of Wrocław ul. Grunwaldzka 53 50-357 Wrocław, Poland

autor

Hotloś, M.

• Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27, PL - 50-370 Wrocław, Poland

autor

Senturk, Z.

• Department of Mathematics Technical University of Istanbul 80626 Maslak, Istanbul, Turkey

Bibliografia

• [1] K. Arslan, R. Deszcz, R. Ezentas, and M. Holloś, On a certain subclass of conformally flat manifolds, Bull. Inst. Math. Acad. Sinica 26 (1998), 283-299.
• [2] A. Besse, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York, 1987.
• [3] J. Deprez, W. Roter, and L. Verstraelen, Conditions on the projective curvature tensor of conformally flat Riemannian manifolds, Kyungpook Math. J. 29 (1989), 153-165.
• [4] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. 44 (1992), Ser. A, Fasc. 1, 1-34.
• [5] R. Deszcz and M. Głogowska, Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 79, 2000.
• [6] R. Deszcz, M. Głogowska, M. Hotloś, D. Kowalczyk, and L. Verstraelen, A review on pseudosymmetry type manifolds, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 84, 1999.
• [7] R. Deszcz, M. Głogowska, M. Hotloś, and Z. Sentürk, On certain quasi-Einstein semisymmetric hypersurfaces, Ann. Univ. Sci. Budapest. 41 (1998), 151-164.
• [8] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, Colloq. Math. 58 (1990), 259-268.
• [9] R. Deszcz and M. Hotloś, On a certain subclass of pseudosymmetric manifolds, Publ. Math. Debrecen 53 (1998), 29-48.
• [10] R. Deszcz, M. Hotloś, and Z. Sentürk, On the equivalence of the Ricci-pseudosymmetry and pseudosymmetry, Colloq. Math. 79 (1999), 211-227.
• [11] R. Deszcz, M. Hotloś, and Z. Sentürk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math., in print.
• [12] R. Deszcz, M. Hotloś, and Z. Sentürk, Quasi-Einstein hypersurfaces in semi-Riemannian spaces of constant curvature, Colloq. Math. 89 (2001), 81-97.
• [13] R. Deszcz, M. Hotloś, and Z. Sentürk, A review of results on quasi-Einstein hypersurfaces in semi-Euclidean spaces, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 78, 2000.
• [14] R. Deszcz and M. Kucharski, On curvature properties of certain generalized Robertson-Walker spacetimes, Tsukuba J. Math. 23 (1999), 113-130.
• [15] R. Deszcz, P. Verheyen, and L. Verstraelen, On some generalized Einstein metric conditions, Publ. Inst. Math. (Beograd) (N.S.) 60 (74) (1996), 108-120.
• [16] R. Deszcz and S. Yaprak, Curvature properties of Carian hypersurfaces, Colloq. Math. 67 (1994), 91-98.
• [17] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying R(X, Y) • R = 0. I. The local version, J. Diff. Geom. 17 (1982), 531-582.
• [18] L. Verstraelen, Comments on pseudosymmetry in the sense of Ryszard Deszcz, in: Geometry and Topology of Submanifolds, VI, World Sci. Publishing, River Edge, NJ, 1994, 199-209.