Resumen de Equivariant tori which are critical points of the conformal total tension functional

M. Barros

• español

  Se obtiene un nuevo método para obtener toros de Willmore en estructuras conformes de Kaluza-Klein sobre fibrados principales con fibra la circunferencia. Diversas aplicaciones de esta técnica son consideradas.

• English

  . We give a new method to obtain Willmore tori over principal circle bundles. This method can be viewed as a reduction of variables criterion for the Willmore variational problem in conformal structures associated with metrics, on principal circle bundles, which are obtained via the generalized inverse Kaluza-Klein mechanism. The problem of finding critical points for the conformal total tension functional in those conformal structures is transfered to the search of critical points for certain elastic energy functionals acting on spaces of curves in the base. This technique is applied to construct wide families of equivariant tori which are critical points for the conformal total tension functional in an ample class of conformal structures.