I am looking for any reference which states, and proves, a Fokker-Planck equation for Riemannian manifolds.
In particular, if $\mathrm{d}X_t=\mu(X_t)~\mathrm{d}t + \sigma(X_t)~\mathrm{d}B_t$ is a stochastic differential equation on a manifold, I want to relate $\mu$ and $\sigma$ to the time evolution of the density of $X_t$, just like the Euclidean Fokker-Planck equation. It would be great if there is a global description of the time evolution, but a local coordinate expression would be okay too.