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

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

2004-10-24

arxiv.org/abs/math/0410498v1

Ergodic Theory and Dynamical Systems 26 (2006) no. 1, 247-266

Mathematics

Differential Geometry

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

Scientific paper

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.

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