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.
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页码：355 / 371
页数：17
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