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Linear Weingarten hypersurfaces in Riemannian space forms

Xiaoli Chao|Peijun Wang
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회보 (Bulletin of the KMS)|제51권 제2호|pp. 567-577

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키워드

maximum principlespace formcircular cylinderlinear Weingarten hypersurfaceClifford torushyperbolic cylinder
주제분류수학

초록

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form Mn+1(c) (c = 1, 0,−1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in Sn+1(1) with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

Abstract

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form Mn+1(c) (c = 1, 0,−1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in Sn+1(1) with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

참고문헌 (17)

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  16. Dan Yang, "LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACE", 대한수학회보, 49(2), pp.271~284 (2012), 대한수학회
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