Rigidity of periodic unstable Lyapunov exponents for Anosov geodesic flows

Let $M$ be a complete Riemannian manifold with finite volume, whose geodesic flow is Anosov. The periodic-exponent rigidity conjecture. If the unstable Lyapunov exponents are constant in all periodic orbits, then $M$ has constant negative sectional curvature.

This conjecture proposes that equality of the unstable Lyapunov exponents along every periodic orbit forces global geometric rigidity, extending the known rigidity result for compact negatively curved manifolds. Its resolution is not specified in the source.