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Strictly non-proportional geodesically equivalent metrics have htop(g) = 0

Published online by Cambridge University Press:  13 January 2006

BORIS S. KRUGLIKOV  and
VLADIMIR S. MATVEEV
BORIS S. KRUGLIKOV
Affiliation:
Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway (e-mail: kruglikov@math.uit.no)
VLADIMIR S. MATVEEV
Affiliation:
Mathematisches Institut der Albert-Ludwigs-Universität, Eckerstraße-1, Freiburg 79104, Germany (e-mail: matveev@email.mathematik.uni-freiburg.de)
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Abstract

If a closed manifold M possesses two Riemannian metrics which have the same unparameterized geodesics and are not strictly proportional at each point, then the topological entropy of both geodesic flows is zero. This is the main result of the paper and it has many dynamical and topological corollaries. In particular, such a manifold M should be finitely covered by the product of a rationally elliptic manifold and a torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 1 , February 2006 , pp. 247 - 266
Copyright
2006 Cambridge University Press

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