On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

Abstract

Solutions of the P. J. Ryan problem as well as investigations of curva- ture properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi- Riemannian space form. These identities, under some assumptions, give rises to new gen- eralized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.