Authors: Bolsinov, Alexey
Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Complete involutive algebras of functions on cotangent bundles of homogeneous spaces
Journal: Mathematische Zeitschrift
Volume: 246
Issue: 1-2
First page: 213
Last page: 236
Issue Date: 1-Jan-2004
Rank: M21
ISSN: 0025-5874
DOI: 10.1007/s00209-003-0596-x
Abstract: 
Homogeneous spaces of all compact Lie groups admit Riemannian metrics with completely integrable geodesic flows by means of C ∞ -smooth integrals. The purpose of this paper is to give some constructions of complete involutive algebras of analytic functions, polynomial in velocities, on the (co)tangent bundles of homogeneous spaces of compact Lie groups. This allows us to obtain new integrable Riemannian and sub-Riemannian geodesic flows on various homogeneous spaces, such as Stiefel manifolds, flag manifolds and orbits of the adjoint actions of compact Lie groups.
Publisher: Springer Link

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