EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 67(81), pp. 103--111 (2000)

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Semisymmetry and Ricci-symmetry for hypersurfaces of semi-Euclidean spaces

Marta D\c abrowska, Filip Defever, Ryszard Deszcz and Dorota Kowalczyk

Department of Mathematics, Agricultural University of Wroclaw, Poland and Department Wiskunde, Katholieke Universiteit Leuven, Belgium

Abstract: In the context of P.J. Ryan's problem on the equivalence of the conditions $R \cdot R = 0$ and $R \cdot S = 0$ for hypersurfaces, we prove that there is indeed equivalence for hypersurfaces of semi-Euclidean spaces in any dimension, under an additional curvature condition of semisymmetric type.

Classification (MSC2000): 53B20; 53B30

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Electronic fulltext finalized on: 21 Dec 2000. This page was last modified: 16 Nov 2001.

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