Comptes Rendus
no. 21-22
Differential Geometry
A Note on surfaces with parallel mean curvature
[Une Note sur des surfaces de courbure moyenne parallèle]

Présenté par : the Editorial Board

Dorel Fetcu1 ; Harold Rosenberg2
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, Volume 349 (2011) no. 21-22, pp. 1195-1197.

Dans cette Note, on étudie des immersions isométriques de surfaces complètes Σ2 dans Mn(c)×R, ou Mn(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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.012
Dorel Fetcu 1 ; Harold Rosenberg 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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Dorel Fetcu; Harold Rosenberg. A Note on surfaces with parallel mean curvature. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1195-1197. doi : 10.1016/j.crma.2011.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.012/

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