Symplectic rigidity of geodesic flows on two-step nilmanifolds1
Symplectic rigidity of geodesic flows on two-step nilmanifolds1
We show that if two 2-step Riemannian nilmanifolds have symplectically conjugate geodesic flows, then they must be isometric. By 2-step Riemannian nilmanifold, we mean a Riemannian manifold of the form (T⧹N, g), where N is a 2-step nilpotent Lie group, Γ is a cocompact discrete subgroup of N, and g …