Conjugacy and rigidity for nonpositively curved manifolds of higher rank

Let M and N be compact Riemannian manifolds with sectional curvature K ⩽ 0 such that M has dimension ⩾ 3 and rank ⩾ 2. If there exists a C0 conjugacy F between the geodesic flows of the unit tangent bundles of M and N, then there exists an isometry G: M → N that induces the same isomorphism as F between the fundamental groups of M and N.