Constant mean curvature Isometric Immersions into 𝕊 2 × and 2 × and related results
Annales de l'Institut Fourier, Online first, 47 p.

In this article, we study constant mean curvature isometric immersions into 𝕊 2 × and 2 × 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 𝔼(κ,τ) and we use the Torralbo–Urbano correspondence to classify the parallel mean curvature surfaces in 𝕊 2 ×𝕊 2 and 2 × 2 with constant intrinsic curvature. It is worthwhile to point out that these classifications provide new examples.

Dans cet article, nous étudions les immersions à courbure moyenne constante dans 𝕊 2 × et 2 × et nous classifions ces immersions quand la surface est à courbure intrinsèque constante. Comme applications, nous utilisons la correspondance des surfaces sœurs pour classifier les surfaces à courbure moyenne constante et courbure intrinsèque constante dans les variétés de dimension 3 homogènes 𝔼(κ,τ) et nous utilisons la correspondance de Torralbo–Urbano pour classifier les surfaces à courbure moyenne parallèle et courbure intrinsèque constante dans 𝕊 2 ×𝕊 2 et 2 × 2 . Il est important de noter que ces classifications fournissent de nouveaux exemples.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3521
Classification: 53C42,  53A10,  53C30
Keywords: Isometric immersions, constant mean curvature surfaces, parallel mean curvature surfaces, homogenous 3-manifolds.
Daniel, Benoît 1; Domingos, Iury 1, 2; Vitório, Feliciano 2

1 Université de Lorraine CNRS, IECL 54000 Nancy (France)
2 Universidade Federal de Alagoas Instituto de Matemática Campus A. C. Simões BR 104 - Norte Km 97 57072-970, Maceió - AL (Brazil)
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Daniel, Benoît; Domingos, Iury; Vitório, Feliciano. Constant mean curvature Isometric Immersions into $\protect \mathbb{S}^2 \times \protect \mathbb{R}$ and $\protect \mathbb{H}^2 \times \protect \mathbb{R}$ and related results. Annales de l'Institut Fourier, Online first, 47 p.

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