Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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

TeX source (27.1K)
DVI (41K)
PostScript (135.8K)

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