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 \(\mathbb{E}^{n+1}_s\). We prove that every conharmonicaly Ricci-symmetric hypersurface \(M\) satisfying the condition \(K \cdot R = 0\) is pseudosymmetric. We also consider the condition \(K \cdot K = LKQ(g, K)\) on hypersurfaces of the semi-Euclidean space \(\mathbb{E}^{n+1}_s\).
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.
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:
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 53C40 | Global submanifolds |
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