Willmore-Like Energies and Elastic Curves with Potential

Abstract

We study invariant Willmore-like tori in total spaces of Killing submersions. In particular, using a relation with elastic curves with potentials in the base surfaces, we analyze Willmore tori in total spaces of Killing submersions. Finally, we apply our findings to construct foliations of these total spaces by constant mean curvature Willmore tori.