HYPERSURFACES WITH CONSTANT CURVATURE QUOTIENTS IN WARPED PRODUCT MANIFOLDS

被引：2

作者：

Wu, Jie ^{[1
]}

Xia, Chao ^{[2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2015年 / 274卷 / 02期

基金：

中国国家自然科学基金; 欧洲研究理事会;

关键词：

constant mean curvature; rigidity; warped product manifold; Gauss-Bonnet curvature; ORDER MEAN-CURVATURE; MAXIMUM PRINCIPLE; SURFACES; UNICITY; TENSOR;

D O I：

10.2140/pjm.2015.274.355

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study rigidity problems for hypersurfaces with constant curvature quotients H2k+1/H-2k in the warped product manifolds. Here H-2k is the k-th Gauss-Bonnet curvature and H2k+1 arises from the first variation of the total integration of H-2k. Hence the quotients considered here are in general different from sigma(2k+1)/sigma(2k), where sigma(k) are the usual mean curvatures. We prove several rigidity and Bernstein-type results for compact or noncompact hypersurfaces corresponding to such quotients.

引用

页码：355 / 371

页数：17

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