Authors: Dragović, Vladimir 
Gajić, Borislav 
Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Singular Manakov flows and geodesic flows on homogeneous spaces of SO(N)
Journal: Transformation Groups
Volume: 14
Issue: 3
First page: 513
Last page: 530
Issue Date: 1-Sep-2009
Rank: M22
ISSN: 1083-4362
DOI: 10.1007/s00031-009-9062-0
Abstract: 
We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k1) ×...× SO(kr), for any choice of k1,...,kr, k1 + ,..., + kr ≤ n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented. Also, the proof of integrability of the SO(n)-invariant Einstein metrics on SO(k1 + k2 + k3)/SO(k1) × SO(k2) × SO(k3) and on the Stiefel manifolds V (n, k) = SO(n)/SO(k) is given.
Publisher: Springer Link

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