3 problems

Let $(M,g)$ be a negatively curved Riemannian manifold, and let $FM$ be its frame bundle. The frame flow is the flow on $FM$ generated by the geodesic-frame vector field, and ergod…

Kanai's conjecture. If the distribution $\mathbb{H}$ is $\mathcal{C}^1$, then $(M,g)$ is locally symmetric.

Let a frame flow be the frame-flow extension of the geodesic flow on a negatively curved Riemannian manifold. Its stable and unstable foliations are generally regular only to limit…