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Metric with ergodic geodesic flow is completely determined by unparameterized geodesics

Authors: Vladimir S. Matveev and Petar J. Topalov
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 98-104
MSC (2000): Primary 53C20; Secondary 37J35, 37C40, 53A20, 53C22, 53B10
Published electronically: December 7, 2000
MathSciNet review: 1796527
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Abstract: Let $g$ be a Riemannian metric with ergodic geodesic flow. Then if some metric $\bar g$ has the same geodesics (regarded as unparameterized curves) with $g$, then the metrics are homothetic. If two metrics on a closed surface of genus greater than one have the same geodesics, then they are homothetic.

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Additional Information

Vladimir S. Matveev
Affiliation: Isaac Newton Institute, Cambridge CB3 0EH, UK
MR Author ID: 609466

Petar J. Topalov
Affiliation: Department of Differential Equations, Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev Street, Bl. 8, Sofia 1113, Bulgaria

Keywords: Projectively equivalent metrics, ergodic geodesic flows
Received by editor(s): June 16, 2000
Published electronically: December 7, 2000
Communicated by: Dmitri Burago
Article copyright: © Copyright 2000 American Mathematical Society