Hypersurfaces satisfying some curvature conditions in the semi-Euclidean space.

*(English)*Zbl 1197.53088Summary: 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 ${\mathbb{E}}_{s}^{n+1}$. We prove that every conharmonicaly Ricci-symmetric hypersurface $M$ satisfying the condition $K\xb7R=0$ is pseudosymmetric. We also consider the condition $K\xb7K=LKQ(g,K)$ on hypersurfaces of the semi-Euclidean space ${\mathbb{E}}_{s}^{n+1}$.

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