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Double quotients of Lie groups with integrable geodesic flow. (English. Russian original) Zbl 0956.53053
Sib. Math. J. 41, No. 3, 419-432 (2000); translation from Sib. Mat. Zh. 41, No. 3, 513-530 (2000).
Double quotients of Lie groups are considered. Using the Thimm method, the author estimates the minimal number of independent integrals of a geodesic flow of double quotients of compact Lie groups with doubleside invariant metrics. The author also proves integrability of geodesic flows on 7- and 13-dimensional spaces of positive sectional curvature obtained by J.-H. Eschenburg and Ya. V. Bazajkin.

MSC:
53D25 Geodesic flows in symplectic geometry and contact geometry
53C30 Differential geometry of homogeneous manifolds
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