Abstract
We obtain a reduction of variables method for the Willmore-Chen variational problem in conformal structures associated with metrics, on principal fibre 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 transferred 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 critical points for the conformal total tension functional in an ample class of stable vacuum states in the Freund-Rubin spontaneous compactification process of the extra dimensions in d = 11 supergravity.
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