Abstract
We prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow and the Poisson bracket deforms due to addition of the Fubini–Study form to the standard symplectic form.
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References
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Thimm A., “Integrable geodesic flows on homogeneous spaces,” Ergodic Theory Dynam. Systems, 1, 495-517 (1981).
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Efimov, D.I. The Magnetic Geodesic Flow in a Homogeneous Field on the Complex Projective Space. Siberian Mathematical Journal 45, 465–474 (2004). https://doi.org/10.1023/B:SIMJ.0000028611.65071.bd
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DOI: https://doi.org/10.1023/B:SIMJ.0000028611.65071.bd