Closed Weingarten hypersurfaces in warped product manifolds

2008/10/18 by Andrade, F., Barbosa, J. L., de Lira, J. H.
#35J60 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0810.3306

Abstract

Given a compact Riemannian manifold M, we consider a warped product M = I ×_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 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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