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.
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José M. Espinar is partially supported by Spanish MEC-FEDER Grant MTM2010-19821, and Regional J. Andalucía Grants P06-FQM-01642 and FQM325.
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Espinar, J.M., Rosenberg, H. When strictly locally convex hypersurfaces are embedded. Math. Z. 271, 1075–1090 (2012). https://doi.org/10.1007/s00209-011-0904-9
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DOI: https://doi.org/10.1007/s00209-011-0904-9