A NEW CHARACTERIZATION OF COMPLETE LINEAR WEINGARTEN HYPERSURFACES IN REAL SPACE FORMS

被引：24

作者：

Aquino, Cicero P. ^{[1
]}

de Lima, Henrique F. ^{[2
]}

Velasquez, Marco A. L. ^{[2
]}

机构：

[1] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil

[2] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58429970 Campina Grande, Paraiba, Brazil

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2013年 / 261卷 / 01期

关键词：

space forms; linear Weingarten hypersurfaces; totally umbilical hypersurfaces; Clifford torus; circular cylinder; hyperbolic cylinder; CONSTANT SCALAR CURVATURE; RIEMANNIAN MANIFOLDS; MEAN-CURVATURE;

D O I：

10.2140/pjm.2013.261.33

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the Hopf's strong maximum principle in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in a real space form Q(c)(n+1) of constant sectional curvature c. 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 isometric to a Clifford torus, if c = 1, a circular cylinder, if c = 0, or a hyperbolic cylinder, if c = -1.

引用

页码：33 / 43

页数：11

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