On certain Ricci-pseudosymmetric hypersurfaces in space forms
by
Marian Hotloś
Institute of Mathematics Wrocaw University of Technology

Curvature properties of hypersurfaces in semi-Riemannian space forms are presented.
First we discuss quasi-Einstein hypersurfaces satisfying certain weak curvature condition of pseudosymmetry type. We prove that such hypersurface must be Ricci-pseudosymmetric and we obtain some relation between scalar curvatures of hypersurface and ambient space.

Next we consider pseudosymmetric hypersurfaces and we find the necessary and sufficient conditions for a such hypersurface to be quasi-Einsteinian. We also give an example of a nonpseudosymmetric Ricci-pseudosymmetric quasi-Einstein hypersurface.

Finally, we consider curvature properties of hypersurfaces satisfying some generalized Einstein metric condition. Our main result states that such hypersurfaces must be Ricci-pseudosymmetric.

Date received: April 26, 2003