Closed Weingarten hypersurfaces in warped product manifolds

Andrade, F.; Barbosa, J. L.; de Lira, J. H.

Closed Weingarten hypersurfaces in warped product manifolds

Authors

Andrade, F.

Barbosa, J. L.

de Lira, J. H.

Description

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.
Paper accepted to publication in Indiana University Mathematics Journal