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.