A Note on surfaces with parallel mean curvature

Fetcu, Dorel; Rosenberg, Harold

doi:10.1016/j.crma.2011.10.012

Differential Geometry

A Note on surfaces with parallel mean curvature
[Une Note sur des surfaces de courbure moyenne parallèle]

Présenté par : the Editorial Board

Fetcu, Dorel ¹ ; Rosenberg, Harold ²

¹ Department of Mathematics, “Gh. Asachi” Technical University of Iasi, Bd. Carol I no. 11, 700506 Iasi, Romania
² IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brasil

Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1195-1197.

Résumé
Abstract

Dans cette Note, on étudie des immersions isométriques de surfaces complètes $Σ^{2}$ dans $M^{n} (c) \times R$ , ou $M^{n} (c)$ est une variété complète simplement connexe de courbure sectionnelle constante c. On classifie ces immersions, lorsque leur vecteur courbure moyenne est parallèle dans le fibré normal et leur courbure intrinsèque est positive ou nulle. Lʼoutil principal est une différentielle quadratique holomorphe dont la partie sans trace satisfait lʼéquation de Codazzi.

We use a Simons type equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.

Reçu le : 2011-02-16
Accepté le : 2011-10-18
Publié le : 2011-11-01

DOI : 10.1016/j.crma.2011.10.012

Affiliations des auteurs :

Fetcu, Dorel ¹ ; Rosenberg, Harold ²

¹ Department of Mathematics, “Gh. Asachi” Technical University of Iasi, Bd. Carol I no. 11, 700506 Iasi, Romania
² IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brasil

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Fetcu, Dorel; Rosenberg, Harold. A Note on surfaces with parallel mean curvature. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1195-1197. doi : 10.1016/j.crma.2011.10.012. http://www.numdam.org/articles/10.1016/j.crma.2011.10.012/

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