Two classes of Riemannian manifolds whose geodesic flows are integrable

DOI10.1090/memo/0619zbMath0904.53007arXivdg-ga/9509004OpenAlexW2076215373MaRDI QIDQ4377870

Kazuyoshi Kiyohara

Publication date: 12 March 1998

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9509004

zbMATH Keywords

classificationLiouville manifoldscompletely integrable geodesic flows\(C_{2\pi}\)-manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Geodesics in global differential geometry (53C22) Hamilton-Jacobi equations in mechanics (70H20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (16)

Conification construction for Kähler manifolds and its application in \(c\)-projective geometry ⋮ The structure of the conjugate locus of a general point on ellipsoids and certain Liouville manifolds ⋮ Geodesic compatibility and integrability of geodesic flows ⋮ Cut loci and conjugate loci on Liouville surfaces ⋮ \(C\)-projective equivalence and integrability of the geodesic flow ⋮ On the integral geometry of Liouville billiard tables ⋮ Four equivalent properties of integrable billiards ⋮ Singular semi-classical approximation on Liouville surfaces ⋮ On Hermite-Liouville manifolds ⋮ On Liouville integrability of $h$-projectively equivalent Kähler metrics ⋮ C-projective geometry ⋮ 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 ⋮ Separability and symmetry operators for Painlevé metrics and their conformal deformations ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces ⋮ Isometric embedding and Darboux integrability ⋮ Manifolds of infinite topological type with integrable geodesic flows

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