On complex structures on two-dimensional tori admitting metrics with nontrivial quadratic integral

DOI10.1007/BF02304996zbMath0865.53030MaRDI QIDQ1922296

Nikolaiĭ N. Nekhoroshev, Ivan K. Babenko

Publication date: 20 October 1996

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Riemannian metricscomplex structures2-torusquadratic integrals

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (6)

Liouville foliations of topological billiards with slipping ⋮ On first integrals of geodesic flows on a two-torus ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ 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 ⋮ Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus

Cites Work

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