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arXiv · 0810.3306

Closed Weingarten hypersurfaces in warped product manifolds

F. Andrade·J. L. Barbosa·J. H. de Lira
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Abstract

Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Rr$. We suppose that the mean curvature of the fibers do not change sign. Given a positive differentiable function $ψ$ in $\bar M$, we find a closed hypersurface $Σ$ which is solution of an equation of the form $F(B)=ψ$, where $B$ is the second fundamental form of $Σ$ and $F$ is a function satisfying certain structural properties. As examples, we may exhibit examples of hypersurfaces with prescribed higher order mean curvature.

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F. Andrade, J. L. Barbosa, J. H. de Lira. 2008-10-18. Closed Weingarten hypersurfaces in warped product manifolds. https://arxiv.org/abs/0810.3306

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