Electronic Research Announcements

Metric with ergodic geodesic flow is completely determined by unparameterized geodesics

Author(s): Vladimir S. Matveev; Petar J. Topalov
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 98-104.
MSC (2000): Primary 53C20; Secondary 37J35, 37C40, 53A20, 53C22, 53B10
Posted: December 7, 2000
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Let

be a Riemannian metric with ergodic geodesic flow. Then if some metric $\bar g$ has the same geodesics (regarded as unparameterized curves) with

, 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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Vladimir S. Matveev
Affiliation: Isaac Newton Institute, Cambridge CB3 0EH, UK
Email: v.matveev@newton.cam.ac.uk

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

DOI: 10.1090/S1079-6762-00-00086-X
PII: S 1079-6762(00)00086-X
Keywords: Projectively equivalent metrics, ergodic geodesic flows
Received by editor(s): June 16, 2000
Posted: December 7, 2000
Communicated by: Dmitri Burago
Copyright of article: Copyright 2000, American Mathematical Society

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