Geodesic
Metric with ergodic geodesic flow is completely determined by unparameterized geodesics
Matveev, Vladimir1 ; Topalov, Petar2
1 Isaac Newton Institute, Cambridge CB3 0EH, UK
2 Department of Differential Equations, Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev Street, Bl. 8, Sofia 1113, Bulgaria
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 98-104.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-00-00086-X

Matveev, Vladimir 1 ; Topalov, Petar 2

1 Isaac Newton Institute, Cambridge CB3 0EH, UK
2 Department of Differential Equations, Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev Street, Bl. 8, Sofia 1113, Bulgaria 
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Matveev, Vladimir; Topalov, Petar. Metric with ergodic geodesic flow is completely determined by unparameterized geodesics. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 98-104. doi : 10.1090/S1079-6762-00-00086-X. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-00-00086-X/

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