# Closed Weingarten hypersurfaces in warped product manifolds - Mathematics > Differential Geometry

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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 themean curvature of the fibers do not change sign. Given a positivedifferentiable function $\psi$ in $\bar M$, we find a closed hypersurface$\Sigma$ which is solution of an equation of the form $FB=\psi$, where $B$ isthe second fundamental form of $\Sigma$ and $F$ is a function satisfyingcertain structural properties. As examples, we may exhibit examples ofhypersurfaces with prescribed higher order mean curvature.

Author: ** F. Andrade, J. L. Barbosa, J. H. de Lira**

Source: https://arxiv.org/