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.
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