Simons Type Equation in ūĚēä 2 √ó‚ĄĚ and ‚Ąć 2 √ó‚ĄĚ and Applications
Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1299-1322.

Let ő£ 2 be an immersed surface in M 2 (c)√ó‚ĄĚ with constant mean curvature. We consider the traceless Weingarten operator ŌÜ 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 ŌÜ and S. By using these equations, we characterize some immersions for which |ŌÜ| or |S| is appropriately bounded.

Soit ő£ 2 une surface immerg√©e dans M 2 (c)√ó‚ĄĚ avec une courbure moyenne constante. Nous consid√©rons l‚Äôop√©rateur de Weingarten √† trace nulle ŌÜ associ√© √† la seconde forme fondamentale de la surface et nous introduisons un tenseur S, li√©s √† la forme quadratique de Abresch-Rosenberg. Nous √©tablissons les √©quations de type Simons pour ŌÜ et S. En utilisant ces √©quations, nous caract√©risons les immersions pour lesquelles |ŌÜ| ou |S| sont born√©s.

DOI: 10.5802/aif.2641
Classification: 53A10,  53C42
Keywords: Surface with constant mean curvature, Simons type equation, Codazzi’s equation
Batista da Silva, M√°rcio Henrique 1

1 Universidade Federal de Alagoas Instituto de Matemática CEP: 57072-900 Maceió - Alagoas (Brazil)
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Batista da Silva, M√°rcio 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, Volume 61 (2011) no. 4, pp. 1299-1322. doi : 10.5802/aif.2641. http://archive.numdam.org/articles/10.5802/aif.2641/

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