4 problems

Let $M$ be a closed manifold which admits a locally symmetric Riemannian metric $g_{loc}$ with nonpositive sectional curvature. Assume that $(M,g_{loc})$ has no local factors isome…

Lyapunov rigidity consequence. Katok's entropy conjecture would imply that $\Lambda_g$ characterizes locally symmetric metrics.

Katok's conjecture. Equality $H=V$ can occur only when $(M,g)$ is a locally symmetric space, equivalently, when $B$ is constant on $SM$. This is an entropy-rigidity conjecture: it…

Let $(Y,F_\Omega)$ be a compact strictly convex real projective manifold of dimension at least $3$, and let $(X,g_0)$ be a hyperbolic structure on the same underlying manifold. Let…