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LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS
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 Title & Authors
LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS
Chao, Xiaoli; Wang, Peijun;
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 Abstract
In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form (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 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
1.
On the Gauss map of Weingarten hypersurfaces in hyperbolic spaces, Bulletin of the Brazilian Mathematical Society, New Series, 2016, 47, 4, 1051  crossref(new windwow)
2.
Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds, Mathematische Nachrichten, 2016, 289, 11-12, 1309  crossref(new windwow)
3.
Linear Weingarten submanifolds in unit sphere, Archiv der Mathematik, 2016, 106, 6, 581  crossref(new windwow)
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