# Problem 38

## Primary tabs

Let $\mathcal M$ be the space of Riemannian metrics on $M$ with volume 1.  What is $\{ h(\varphi_1), \varphi {\textrm { geodesic flow of }}\; g: g \in \mathcal M\}$? What is the relation with topological invariants of $M$?

## Tags

See [1].

### References

1. [besson1995entropies] Besson G, Courtois G, Gallot S.  1995.  Geometric and functional analysis. 5:731–799.