On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms
Volume 96 / 2003
Colloquium Mathematicum 96 (2003), 149-166
MSC: 53B20, 53B25, 53B30, 53B50, 53C25, 53C40.
DOI: 10.4064/cm96-2-1
Abstract
Solutions of the P. J. Ryan problem as well as investigations of curvature 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 generalized Einstein metric conditions on $M$. We investigate hypersurfaces satisfying such curvature conditions.
