The moduli space of 2-step nilpotent Lie algebras of type (p,q

Introduction Simply connected homogeneous Riemannian manifolds with negative sectional curvature are closely connected with nilpotent Lie algebras, and if the sectional curvature is normalized to satisfy the inequalities − 4 ≤ K ≤ −1 (quarter pinched), then the connection is with 2-step nilpotent Lie algebras. In particular, any 2-step nilpotent Lie algebra N gives rise to a homogeneous Riemannian manifold whose sectional curvature i