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A maximum principle for complete hypersurfaces in locally symmetric Riemannian manifold

Shicheng Zhang
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회논문집 (Communications of the KMS)|제29권 제1호|pp. 141-153

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참고문헌

키워드

totally umbilicallocally symmetriclinear Weingarten hypersurfaces
주제분류수학

초록

In this article, we apply the weak maximumprinciple in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

Abstract

In this article, we apply the weak maximumprinciple in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

참고문헌 (26)

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