Geodesic equivalence of metrics as a particular case of integrability of geodesic flows

DOI10.1007/BF02551397zbMath0996.53054MaRDI QIDQ1592124

Peter J. Topalov, Vladimir S. Matveev

Publication date: 29 October 2002

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Laplace-Beltrami operatorintegrable geodesic flowsgeodesically equivalent metricsJFM 27.0603.04orbitally equivalent metrics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesics in global differential geometry (53C22) Geodesic flows in symplectic geometry and contact geometry (53D25)

Cites Work

• Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid
• CONSTRUCTION OF COMPLETELY INTEGRABLE GEODESIC FLOWS ON COMPACT SYMMETRIC SPACES
• TOPOLOGICAL OBSTRUCTIONS TO INTEGRABILITY OF GEODESIC FLOWS ON NON-SIMPLY-CONNECTED MANIFOLDS
• Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
• Conjugate points of hyperbolic geodesics of square integrable geodesic flows on closed surfaces

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