On Ricci-pseudosymmetric hypersurfaces in space forms

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

Abstrakty

EN

We investigate curvature properties of hypersurfaces in semi-Riemannian space forms satisfying some curvature condition of pseudosymmetry type. Our main result states that such hypersurfaces must be Ricci-pseudosymmetric.

Słowa kluczowe

EN

pseudosymmetry type manifold; Ricci-type equation; Cartan hypersurface

PL

powierzchnia Cartana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 1
• Strony: 203--214
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Deszcz R.

• Department of Mathematics, Agricultural University, Grunwaldzka 53, 50-357 Wroclaw, Poland

autor

Hotloś M.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-357 Wrocław, Poland

autor

Şentürk Z.

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

Bibliografia

• [1] M. Belkhelfa, R. Deszcz, M. Głogowska, M. Hotloś, D. Kowalczyk, L. Verstraelen, A review on pseudosymmetry type manifolds, in: Banach Center Publ. 57, Inst. Math., Polish. Acad. Sci. (2002), 179-194.
• [2] F. Defever, R. Deszcz, P. Dhooghe, L. Verstraelen, Ş. Yaprak, On Ricci-pseudosymmetric hypersurfaces in spaces of constant curvature, Results in Math. 27 (1995), 227-236.
• [3] R. Deszcz, M. Głogowska, Some nonsemisymmetric Ricci-semisymmetric warped product hypersurfaces, Publ. Inst. Math. (Beograd) (N.S.) 76(86) (2002), 81-93.
• [4] R. Deszcz, M. Głogowska , M. Hotloś, L. Verstraelen, On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms, Colloq. Math. 96 (2003), 149-166.
• [5] R. Deszcz, M. Hotloś, On a certain subclass of pseudosymmetric manifolds, Publ. Math. Debrecen 53 (1998), 29-48.
• [6] R. Deszcz, M. Hotloś, On some pseudosymmetry type curvature condition, Tsukuba J. Math. 27 (2003), 13-30.
• [7] R. Deszcz, M. Hotloś, Z. Şentürk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow Math . 27 (2001), 375-389.
• [8] R. Deszcz, M. Hotloś, Z. Şentürk, On curvature properties of certain quasi-Einstein hypersurfaces, Dept. Math. Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 104, 2002.
• [9] R. Deszcz, D. Kowalczyk, On some class of pseudosymmetric warped products, Colloq. Math. 97 (2003), 7-22.
• [10] R. Deszcz, L. Verstraelen, Ş. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica 22 (1994), 167-179.
• [11] M. Głogowska, On a curvature characterization of Ricci-pseudosymmetric hypersurfaces, Dept. Math. Agricultural Univ. Wroclaw, Ser. A, Theory and Methods, Report No. 97, 2001.