대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권1호
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  • Pages.141-153
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  • 2014
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A MAXIMUM PRINCIPLE FOR COMPLETE HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLD

  • Zhang, Shicheng (School of Mathematics and Statistics Jiangsu Normal University)
  • 투고 : 2013.05.09
  • 발행 : 2014.01.31
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초록

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten 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.

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참고문헌

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