Murathan, Cengizhan; Arslan, Kadri; Deszcz, Ryszard; Ezentaṣ, Ridvan; Özgür, Cihan On some class of hypersurfaces of semi-Euclidean spaces. (English) Zbl 1012.53017 Publ. Math. Debr. 58, No. 4, 587-604 (2001). 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. Reviewer: Péter T.Nagy (Debrecen) Cited in 2 Documents MSC: 53B20 Local Riemannian geometry 53B25 Local submanifolds 53B50 Applications of local differential geometry to the sciences Keywords:pseudosymmetry type manifold; Ricci-semisymmetric manifold; semisymmetric manifold; hypersurface PDFBibTeX XMLCite \textit{C. Murathan} et al., Publ. Math. Debr. 58, No. 4, 587--604 (2001; Zbl 1012.53017)