

Preprint 20/2014
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
Bibtex
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 Lk. To achieve
this, we develop some new kind of Newton-Maclaurin type inequalities on Lk which may have
independent interest.