On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds

2013/12/18 by Jie Wu, Chao Xia, Wu, Jie +1
Mathematics · #53C40 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Primary 53C24 #Secondary 52A20

paper · pdf · doi:10.48550/arxiv.1312.5152

openalex publication_date 2013/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work \citeMon, Brendle,BE considering constant mean curvature functions. Secondly, we obtain the rigidity results for hypersurfaces in the space forms with constant linear combinations of intrinsic Gauss-Bonnet curvatures L_k. To achieve this, we develop some new kind of Newton-Maclaurin type inequalities on L_k which may have independent interest.

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