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Complete hypersurfaces with $ RS=0$ in $ E\sp{n+1}$


Author: Yoshio Matsuyama
Journal: Proc. Amer. Math. Soc. 88 (1983), 119-123
MSC: Primary 53B25; Secondary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1983-0691290-9
MathSciNet review: 691290
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Abstract: A locally symmetric Riemannian manifold satisfies $ RR = 0$ and in particular $ RS = 0$. The purpose of this paper is to show that the conditions $ RR = 0$ and $ RS = 0$ are equivalent for complete hypersurfaces in $ {E^{n + 1}}$ and to give by $ RS = 0$ some characterizations of locally symmetric hypersurfaces in $ {E^{n + 1}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0691290-9
Keywords: Hypersurfaces, curvature tensor, Ricci tensor, complete
Article copyright: © Copyright 1983 American Mathematical Society

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