Abstract
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 is a metric whose pullback to N is left invariant.
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