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

Inês Silva de Oliveira; Paul A. Schweitzer S. J

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

Differential Geometry 2012-05-03 v1

Authors: Inês Silva de Oliveira , Paul A. Schweitzer S. J

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.

Keywords

locally convex hypersurfaces Hadamard-Stoker theorem hyperbolic space vertical graph simple end immersion embedding

Cite

@article{arxiv.1205.0470,
  title  = {Locally convex hypersurfaces immersed in $H^n \times R$},
  author = {Inês Silva de Oliveira and Paul A. Schweitzer S. J},
  journal= {arXiv preprint arXiv:1205.0470},
  year   = {2012}
}

Comments

18 pages, 6 figures

Related papers

View all related →