Authors: Fedorov, Yuri
Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Geodesic flows and Neumann systems on Stiefel varieties: Geometry and integrability
Journal: Mathematische Zeitschrift
Volume: 270
Issue: 3-4
First page: 659
Last page: 698
Issue Date: 1-Apr-2012
Rank: M21
ISSN: 0025-5874
DOI: 10.1007/s00209-010-0818-y
Abstract: 
We study integrable geodesic flows on Stiefel varieties V n,r = SO(n)/SO(n-r) given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on V n,r with the above metrics and proves their integrability in the non-commutative sense by presenting compatible Poisson brackets on (T *V n,r)/SO(r). Various reductions of the latter systems are described, in particular, the generalized Neumann system on an oriented Grassmannian G n,r and on a sphere S n-1 in presence of Yang-Mills fields or a magnetic monopole field. Apart from the known Lax pair for generalized Neumann systems, an alternative (dual) Lax pair is presented, which enables one to formulate a generalization of the Chasles theorem relating the trajectories of the systems and common linear spaces tangent to confocal quadrics. Additionally, several extensions are considered: the generalized Neumann system on the complex Stiefel variety W n,r = U(n)/U(n-r), the matrix analogs of the double and coupled Neumann systems.
Publisher: Springer Link

Show full item record

SCOPUSTM   
Citations

11
checked on Nov 27, 2022

Page view(s)

18
checked on Nov 28, 2022

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.