Energy‐minimizing mappings of real projective spaces

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