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On semi-Riemannian manifolds satisfying some conformally invariant curvature condition

We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to 4-dimensional warped products.

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

Ryszard DeszczMałgorzata GłogowskaMarian HotlośLeopold Verstraelen — 2003

Colloquium Mathematicae

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.

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