When strictly locally convex hypersurfaces are embedded
Abstract
In this paper we will prove HadamardStoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a $1/4$pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That is, under the condition that the principal curvatures of an immersed hypersurfaces are greater than some nonnegative constant (depending on the ambient space), we prove that such a hypersurface is embedded and we also study its topology.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1003.0101
 Bibcode:
 2010arXiv1003.0101E
 Keywords:

 Mathematics  Differential Geometry