Constant mean curvature Isometric Immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and related results - Université de Lorraine Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Constant mean curvature Isometric Immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and related results

Résumé

In this article, we study constant mean curvature isometric immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and we classify these isometric immersions when the surface has constant intrinsic curvature. As applications, we use the sister surface correspondence to classify the constant mean curvature surfaces with constant intrinsic curvature in the $3-$dimensional homogenous manifolds $\mathbb{E}(\kappa, \tau)$ and we use the Torralbo-Urbano correspondence to classify the parallel mean curvature surfaces in $\mathbb{S}^2 \times \mathbb{S}^2$ and $\mathbb{H}^2 \times \mathbb{H}^2$ with constant intrinsic curvature. It is worthwhile to point out that these classifications provide new examples.

Dates et versions

hal-03267842 , version 1 (22-06-2021)

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Citer

Benoit Daniel, Iury Domingos, Feliciano Vitório. Constant mean curvature Isometric Immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and related results. 2019. ⟨hal-03267842⟩
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