Total mean curvature surfaces in the product space ${\mathbb{S}}^n\times \mathbb{R}$ and applications

Alma L. Albujer, Sylvia F. da Silva, Fábio R. dos Santos

The total mean curvature functional for submanifolds into the Riemannian product space ${\mathbb{S}}^n\times \mathbb{R}$ is considered and its first variational formula is presented.…