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Hypersurfaces satisfying some curvature conditions in the semi-Euclidean space. (English) Zbl 1197.53088

Summary: 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 the condition K·K=LKQ(g,K) on hypersurfaces of the semi-Euclidean space 𝔼 s n+1 .

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
53C50Lorentz manifolds, manifolds with indefinite metrics
53C40Global submanifolds (differential geometry)