Hypersurfaces satisfying some curvature conditions in the semi-Euclidean space

Abstract

We consider some conditions on conharmonic curvature tensor K. which has many applications in physics and mathematics, on a hypersurface in the semi-Euclidean space E(s)(n+1). We prove that every conharmonicaly Ricci-symmetric hypersurface M satisfying the condition K . R = 0 is pseudosymmetric. We also consider K . K = L(k)Q(g.K) on hypersurface of the semi-Euclidean space E(s)(n+1).