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On some class of hypersurfaces of semi-Euclidean spaces. (English) Zbl 1012.53017

The paper is devoted to the investigation of semisymmetric and Ricci-semisymmetric hypersurfaces of semi-Euclidean spaces. A (semi-)Riemannian manifold is semisymmetric if \(R\cdot R=0\), it is Ricci-semisymmetric if \(R\cdot S=0\) where the tensor fields \(R\) and \(S\) denote the curvature and the Ricci curvature tensor. Sufficient conditions for hypersurfaces of semi-Riemannian manifolds are given which guarantee their semisymmetric or Ricci semisymmetric property. The results are generalizations of previous theorems of some of the authors and their collaborators.

MSC:

53B20 Local Riemannian geometry
53B25 Local submanifolds
53B50 Applications of local differential geometry to the sciences
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