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
DOI:
https://doi.org/10.1090/S1079-6762-00-00086-X
Published electronically:
December 7, 2000
MathSciNet review:
1796527
Full-text PDF Free Access
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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
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
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
