Abstract
Let G/K be an orbit of the adjoint representation of a compact connected Lie group G, σ be an involutive automorphism of G and \( \tilde{G} \) be the Lie group of fixed points of σ. We find a sufficient condition for the complete integrability of the geodesic ow of the Riemannian metric on \( \tilde{G}/\left(\tilde{G}\cap K\right) \) which is induced by the bi-invariant Riemannian metric on \( \tilde{G} \). The integrals constructed here are real analytic functions, polynomial in momenta. It is checked that this sufficient condition holds when G is the unitary group U(n) and σ is its automorphism determined by the complex conjugation.
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(IHOR V. MYKYTYUK) This research is partially supported by the Ministry of Economy and Competitiveness, Spain - CSIC, under Project MTM2011-22528.
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MYKYTYUK, I.V. INTEGRABILITY OF GEODESIC FLOWS FOR METRICS ON SUBORBITS OF THE ADJOINT ORBITS OF COMPACT GROUPS. Transformation Groups 21, 531–553 (2016). https://doi.org/10.1007/s00031-016-9373-x
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DOI: https://doi.org/10.1007/s00031-016-9373-x