Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 094, 19 pages      arXiv:2201.09576      https://doi.org/10.3842/SIGMA.2022.094

Equivalent Integrable Metrics on the Sphere with Quartic Invariants

Andrey V. Tsiganov
St. Petersburg State University, St. Petersburg, Russia

Received March 31, 2022, in final form December 04, 2022; Published online December 06, 2022

Abstract
We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can construct new integrable systems on the sphere with quartic invariants.

Key words: integrable metrics; canonical transformations; two-dimensional sphere.

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