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

Abstract

Equations of Simons type are presented. They are satisfied by a pair of special operators associated to the immersion ${\Sigma }^2\looparrowright M^2(c)\times \mathbb{R}$ with constant mean curvature. Some immersions are characterized.

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