Geodesic equivalence of metrics on surfaces, and their integrability.

zbMath1041.37502MaRDI QIDQ1594491

Vladimir S. Matveev, Peter J. Topalov

Publication date: 28 January 2001

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsgeodesic flowcompletely integrable systemsgeodesic equivalence of metrics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geodesic flows in symplectic geometry and contact geometry (53D25) Projective differential geometry (53A20)

Related Items (10)

Projectively equivalent metrics on the torus ⋮ The eigenvalues of the Sinyukov mapping for geodesically equivalent metrics are globally ordered ⋮ Two-dimensional metrics admitting precisely one projective vector field ⋮ On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 ⋮ A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields ⋮ Differential invariants for cubic integrals of geodesic flows on surfaces ⋮ Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two ⋮ Complete Einstein metrics are geodesically rigid ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics

This page was built for publication: Geodesic equivalence of metrics on surfaces, and their integrability.