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

Boris S. Kruglikov; Vladimir S. Matveev

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

Boris S. Kruglikov·Vladimir S. Matveev

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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.

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BibTeX RIS

Boris S. Kruglikov, Vladimir S. Matveev. 2004-10-24. Strictly non-proportional geodesically equivalent metrics have $h_\text{top}(g)=0$. https://arxiv.org/abs/math/0410498

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