Geodesic hierarchies and involutivity

DOI10.1063/1.1379068zbMath1005.37027OpenAlexW2088167864MaRDI QIDQ2775004

Peter J. Topalov

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1379068

zbMATH Keywords

geodesic flowsLiouville integrabilitypseudo-Riemannian 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)

Related Items (6)

Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures ⋮ On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies. ⋮ Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two ⋮ Discrete analog of the projective equivalence and integrable billiard tables ⋮ On Liouville integrability of $h$-projectively equivalent Kähler metrics ⋮ Complete Einstein metrics are geodesically rigid

Cites Work

• Trajectory equivalence and corresponding integrals
• Integrability criterion of geodesical equivalence: hierarchies
• Families of metrics geodesically equivalent to the analogs of the Poisson sphere
• Tensor invariants of natural mechanical systems on compact surfaces, and the corresponding integrals

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