When strictly locally convex hypersurfaces are embedded

@article{Espinar2010WhenSL,
  title={When strictly locally convex hypersurfaces are embedded},
  author={Jos'e M. Espinar and Harold Rosenberg},
  journal={Mathematische Zeitschrift},
  year={2010},
  volume={271},
  pages={1075-1090}
}
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… 
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