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http://dx.doi.org/10.4134/BKMS.2014.51.2.567

LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS  

Chao, Xiaoli (Department of Mathematics Southeast University)
Wang, Peijun (Department of Mathematics Southeast University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 567-577 More about this Journal
Abstract
In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form $\mathbb{M}^{n+1}(c)$ (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 $\mathbb{S}^{n+1}(1)$ 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.
Keywords
linear Weingarten hypersurface; maximum principle; space form; Clifford torus; circular cylinder; hyperbolic cylinder;
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Times Cited By KSCI : 2  (Citation Analysis)
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