IUMJ

Title: Closed Weingarten hypersurfaces in warped product manifolds

Authors: Francisco J. de Andrade, Joao L. M. Barbosa and Jorge H. S. de Lira

Issue: Volume 58 (2009), Issue 4, 1691-1718

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 $\mathbb{R}$. We suppose that the mean curvature of the fibers does not change sign. Given a positive differentiable function $\psi$ in $\bar{M}$, we find a closed hypersurface $\Sigma$ which is solution of an equation of the form $F(B) = \psi$, where $B$ is the second fundamental form of $\Sigma$ and $F$ is a function satisfying certain structural properties. As examples, we may exhibit examples of hypersurfaces with prescribed higher order mean curvature.