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

Jie Wu and Chao Xia

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Submission date: 18. Feb. 2014
Pages: 26
published in: Annals of global analysis and geometry, 46 (2014) 1, p. 1-22 
DOI number (of the published article): 10.1007/s10455-013-9405-x
MSC-Numbers: 53C24, 52A20, 53C40
Keywords and phrases: constant mean curvature, warped product manifold, Gauss-Bonnet curvature
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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 of Brendle-Eichmair and Montiel 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.