Energy-minimizing mappings of real projective spaces

Abstract

We give a sharp lower bound for the energy in homotopy classes of mappings from real projective space to Riemannian manifolds, together with an upper bound for its infimum. We characterize the maps which attain this lower bound for energy, and we explain how the infimum of the energy in a homotopy class of mappings of real projective n-space is determined by an associated class of mappings of the real projective plane.