When strictly locally convex hypersurfaces are embedded

Details When strictly locally convex hypersurfaces are embedded When strictly locally convex hypersurfaces are embedded

2010-02-27

arxiv.org/abs/1003.0101v1

Mathematics

Differential Geometry

Scientific paper

In this paper we will prove Hadamard-Stoker 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 non-negative constant (depending on the ambient space), we prove that such a hypersurface is embedded and we also study its topology.

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