Simons Type Equation in 𝕊 2 × and 2 × and Applications  [ Les équations de type Simons dans 𝕊 2 × et 2 × et applications ]
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, p. 1299-1322
Soit Σ 2 une surface immergée dans M 2 (c)× 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)× 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 : https://doi.org/10.5802/aif.2641
Classification:  53A10,  53C42
Mots clés: surface à courbure moyenne constante, équation type Simons, équation de Codazzi
@article{AIF_2011__61_4_1299_0,
     author = {Batista da Silva, M\'arcio Henrique},
     title = {Simons Type Equation in $\mathbb{S}^{2}\times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ and Applications},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {4},
     year = {2011},
     pages = {1299-1322},
     doi = {10.5802/aif.2641},
     mrnumber = {2951494},
     zbl = {1242.53066},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_4_1299_0}
}
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. http://www.numdam.org/item/AIF_2011__61_4_1299_0/

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