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arXiv · 1601.06619

Embeddedness of spheres in homogeneous three-manifolds

William H. Meeks III·Pablo Mira·Joaquín Pérez
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Abstract

Let $X$ denote a metric Lie group diffeomorphic to $\mathbb{R}^3$ that admits an algebraic open book decomposition. In this paper we prove that if $Σ$ is an immersed surface in $X$ whose left invariant Gauss map is a diffeomorphism onto $\mathbb{S}^2$, then $Σ$ is an embedded sphere. As a consequence, we deduce that any constant mean curvature sphere of index one in $X$ is embedded.

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William H. Meeks III, Pablo Mira, Joaquín Pérez. 2016-01-25. Embeddedness of spheres in homogeneous three-manifolds. https://arxiv.org/abs/1601.06619

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