Singular Manakov Flows and Geodesic Flows on Homogeneous Spaces

Vladimir Dragovic; Borislav Gajic; Bozidar Jovanovic

doi:10.1007/s00031-009-9062-0

Singular Manakov Flows and Geodesic Flows on Homogeneous Spaces

Mathematical Physics 2010-03-23 v2 Differential Geometry math.MP Exactly Solvable and Integrable Systems

Authors: Vladimir Dragovic , Borislav Gajic , Bozidar Jovanovic

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces $SO(n)/SO(k_1)\times...\times SO(k_r)$ , for any choice of $k_1,...,k_r$ , $k_1+...+k_r\le n$ . 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 $SO(k_1+k_2+k_3)/SO(k_1)\times SO(k_2)\times SO(k_3)$ and on the Stiefel manifolds $V(n,k)=SO(n)/SO(k)$ is given.

Cite

@article{arxiv.0901.2444,
  title  = {Singular Manakov Flows and Geodesic Flows on Homogeneous Spaces},
  author = {Vladimir Dragovic and Borislav Gajic and Bozidar Jovanovic},
  journal= {arXiv preprint arXiv:0901.2444},
  year   = {2010}
}

Comments

17 pages, minor changes

Singular Manakov Flows and Geodesic Flows on Homogeneous Spaces

Abstract

Cite

Comments

Related papers