zbMATH — the first resource for mathematics

On Ricci-pseudosymmetric hypersurfaces in space forms. (English) Zbl 1055.53011
This paper continues earlier work of the authors – with various coauthors – on a special class of hypersurfaces in semi-Riemannian spaces of constant curvature. The formal definition of this class, called Ricci-pseudosymmetric hypersurfaces, is too involved to be given here; as the name suggests, it is an algebraic condition on the Ricci tensor. The purpose of the present paper is to show that two other curvature conditions, for hypersurfaces in semi-Riemannian spaces of constant curvature, are equivalent to the condition of being Ricci-pseudosymmetric.

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
Full Text: DOI