On some class of hypersurfaces of semi-Euclidean spaces (Q2754956)

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.