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- Title
When strictly locally convex hypersurfaces are embedded.
- Authors
Espinar, José; Rosenberg, Harold
- Abstract
In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $${\mathcal{M}^n \times \mathbb{R}}$$, where $${\mathcal{M}^n}$$ 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 hypersurface 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.
- Subjects
CONVEX functions; HYPERSURFACES; TOPOLOGY; MANIFOLDS (Mathematics); SUBMERSIONS (Mathematics)
- Publication
Mathematische Zeitschrift, 2012, Vol 271, Issue 3/4, p1075
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0904-9