English

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

Differential Geometry 2011-08-08 v1 Mathematical Physics math.MP

Abstract

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

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Cite

@article{arxiv.math/0410498,
  title  = {Strictly non-proportional geodesically equivalent metrics have $h_\text{top}(g)=0$},
  author = {Boris S. Kruglikov and Vladimir S. Matveev},
  journal= {arXiv preprint arXiv:math/0410498},
  year   = {2011}
}

Comments

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