Strictly non-proportional geodesically equivalent metrics have h_top(g)=0
classification
🧮 math.DG
math-phmath.MP
keywords
equivalentgeodesicallymetricsnon-proportionalstrictlyclosedconnectedentropy
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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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