Strictly non-proportional geodesically equivalent metrics have $h_{\text{top}}(g)=0$

Abstract

Suppose the Riemannian metrics $g$ and $\bar{g}$ on a closed connected manifold $M^n$ are geodesically equivalent and strictly non-proportional at least at one point. Then the topological entropy of the geodesic flow of $g$ vanishes.

arXiv commentThis is a slightly extended version of the paper submitted to ETDS. 16 pages, one .eps figure

References in corpus (1)

• Invariant fibration of geodesic flows