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MiS Preprint
20/2014

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

Jie Wu and Chao Xia

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.

Received:
Feb 18, 2014
Published:
Feb 25, 2014
MSC Codes:
53C24, 52A20, 53C40
Keywords:
constant mean curvature, warped product manifold, Gauss-Bonnet curvature

Related publications

inJournal
2014 Repository Open Access
Jie Wu and Chao Xia

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

In: Annals of global analysis and geometry, 46 (2014) 1, pp. 1-22