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

Abstract : 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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.univ-lorraine.fr/hal-03267842
Contributor : Benoît Daniel Connect in order to contact the contributor
Submitted on : Tuesday, June 22, 2021 - 4:52:25 PM
Last modification on : Friday, January 7, 2022 - 3:21:08 PM

### Identifiers

• HAL Id : hal-03267842, version 1
• ARXIV : 1911.12630

### Citation

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⟩

Record views