no. 4
Simons Type Equation in 𝕊 2 ×ℝ and ℍ 2 ×ℝ and Applications
[Les équations de type Simons dans 𝕊 2 ×ℝ et ℍ 2 ×ℝ et applications]
Batista da Silva, Márcio Henrique1
1 Universidade Federal de Alagoas Instituto de Matemática CEP: 57072-900 Maceió - Alagoas (Brazil)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1299-1322.

Soit Σ 2 une surface immergée dans M 2 (c)×ℝ avec une courbure moyenne constante. Nous considérons l’opérateur de Weingarten à trace nulle φ associé à la seconde forme fondamentale de la surface et nous introduisons un tenseur S, liés à la forme quadratique de Abresch-Rosenberg. Nous établissons les équations de type Simons pour φ et S. En utilisant ces équations, nous caractérisons les immersions pour lesquelles |φ| ou |S| sont bornés.

Let Σ 2 be an immersed surface in M 2 (c)×ℝ with constant mean curvature. We consider the traceless Weingarten operator φ associated to the second fundamental form of the surface, and we introduce a tensor S, related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both φ and S. By using these equations, we characterize some immersions for which |φ| or |S| is appropriately bounded.

DOI : 10.5802/aif.2641
Classification : 53A10, 53C42
Keywords: Surface with constant mean curvature, Simons type equation, Codazzi’s equation
Mots-clés : surface à courbure moyenne constante, équation type Simons, équation de Codazzi

Batista da Silva, Márcio Henrique 1

1 Universidade Federal de Alagoas Instituto de Matemática CEP: 57072-900 Maceió - Alagoas (Brazil) 
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Batista da Silva, Márcio Henrique. Simons Type Equation in $\mathbb{S}^{2}\times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ and Applications. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1299-1322. doi : 10.5802/aif.2641. https://aif.centre-mersenne.org/articles/10.5802/aif.2641/

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