Singular Manakov flows and geodesic flows on homogeneous spaces of SO(N)

被引：0
作者：
V. Dragović
B. Gajić
B. Jovanović
机构：
[1] Mathematical Institute SANU,
[2] GFM,undefined
[3] Univ. of Lisbon,undefined
来源：
Transformation Groups | 2009年 / 14卷
关键词：
Homogeneous Space; Poisson Bracket; Einstein Metrics; Symplectic Leaf; Adjoint Orbit;
D O I：
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学科分类号：
摘要：
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.
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页码：513 / 530
页数：17
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