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Metric with ergodic geodesic flow is completely determined by unparameterized geodesics
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Metric with ergodic geodesic flow is completely determined by unparameterized geodesics
Vladimir S. Matveev and Petar J. Topalov
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.
Copyright 2000 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 06 (2000), pp. 98-104
- Publisher Identifier: S 1079-6762(00)00086-X
- 2000 Mathematics Subject Classification. Primary 53C20; Secondary 37J35, 37C40, 53A20, 53C22, 53B10
- Key words and phrases. Projectively equivalent metrics, ergodic geodesic flows
- Received by the editors June 16, 2000
- Posted on December 7, 2000
- Communicated by Dmitri Burago
- Comments (When Available)
Vladimir S. Matveev
Isaac Newton Institute, Cambridge CB3 0EH, UK
E-mail address: v.matveev@newton.cam.ac.uk
Petar J. Topalov
Department of Differential Equations, Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev Street, Bl. 8, Sofia 1113, Bulgaria
E-mail address: topalov@math.bas.bg
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