Critical Homogeneous Metrics on the Heisenberg Manifold

Abstract

Let H be the Heisenberg group and let Γ be the discrete subgroup of H with integer entries. We obtain a necessary and sufficient condition for a homogeneous metric g on H⁄Γ to be a critical point for the total scalar curvature functional I defined for the set A(M) of some proper homogeneous Riemannian metrics on H⁄Γ.