Locally convex hypersurfaces immersed in $H^n\times R$

Abstract

We prove a theorem of Hadamard-Stoker type: a connected locally convex complete hypersurface immersed in $H^n\times R$ (n>1), where $H^n$ is n-dimensional hyperbolic space, is embedded and homeomorphic either to the n-sphere or to $R^n$. In the latter case it is either a vertical graph over a convex domain in $H^n$ or has what we call a simple end.

18 pages, 6 figures

References in corpus (2)

• When strictly locally convex hypersurfaces are embedded
• Locally convex surfaces immersed in a Killing submersion