LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS

Chao, Xiaoli; Wang, Peijun

doi:10.4134/BKMS.2014.51.2.567

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LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS

Journal title : Bulletin of the Korean Mathematical Society
Volume 51, Issue 2, 2014, pp.567-577
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2014.51.2.567

Title & Authors

LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS
Chao, Xiaoli; Wang, Peijun;

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;

Language

English

Cited by

3time(s) in CrossRef

On the Gauss map of Weingarten hypersurfaces in hyperbolic spaces, Bulletin of the Brazilian Mathematical Society, New Series, 2016, 47, 4, 1051

Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds, Mathematische Nachrichten, 2016, 289, 11-12, 1309

Linear Weingarten submanifolds in unit sphere, Archiv der Mathematik, 2016, 106, 6, 581

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