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 and on a closed connected manifold are geodesically equivalent and strictly non-proportional at least at one point. Then the topological entropy of the geodesic flow of vanishes.
Keywords
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