# 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…

## 9 Citations

Locally convex hypersurfaces immersed in $H^n \times R$

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We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where…

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Let $$ M^{n+1} $$ M n + 1 ( $$ n \ge 2 $$ n ≥ 2 ) be a simply-connected space form of sectional curvature $$ -\kappa ^2 $$ - κ 2 for some $$ \kappa \ge 0 $$ κ ≥ 0 , and I an interval not containing…

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In this article, we study complete surfaces $\Sigma$, isometrically immersed in the product space $\mathbb{H}^2\times\mathbb{R}$ or $\mathbb{S}^2\times\mathbb{R}$ having positive extrinsic curvature…

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The main point of this paper is that, under suitable conditions on the mean curvature and the Ricci curvature of the ambient space, we can extend Choi-Schoen's Compactness Theorem to compact embedded…

Weingarten Type Surfaces in ℍ2 × ℝ and 𝕊2 × ℝ

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Abstract In this article, we study complete surfaces $\sum $ , isometrically immersed in the product spaces ${{\mathbb{H}}^{2}}\,\times \,\mathbb{R}$ or ${{\mathbb{S}}^{2\,}}\times \,\mathbb{R}$…

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