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Simons Type Equation in $𝕊^{2} \times ℝ$ and $ℍ^{2} \times ℝ$ and Applications

Márcio Henrique Batista da Silva — 2011

Annales de l’institut Fourier

Let $Σ^{2}$ be an immersed surface in $M^{2} (c) \times ℝ$ 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.

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Simons Type Equation in 𝕊 2 × ℝ and ℍ 2 × ℝ and Applications

Simons Type Equation in $𝕊^{2} \times ℝ$ and $ℍ^{2} \times ℝ$ and Applications