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Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability
dc.contributor.author | Fedorov, Yuri |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2011-03-21T12:34:38Z |
dc.date.available | 2011-03-21T12:34:38Z |
dc.date.created | 2010-12-03 |
dc.date.issued | 2010-12-03 |
dc.identifier.citation | Fedorov, Y. Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability. "Mathematische Zeitschrift", 03 Desembre 2010, p. 1-40. |
dc.identifier.issn | 0025-5874 |
dc.identifier.uri | http://hdl.handle.net/2117/11987 |
dc.description.abstract | We study integrable geodesic flows on Stiefel varieties Vn,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 Vn,r with the above metrics and proves their integrability in the non-commutative sense by presenting compatible Poisson brackets on (T ∗Vn,r )/SO(r ). Various reductions of the latter systems are described, in particular, the generalized Neumann system on an oriented Grassmannian Gn,r and on a sphere Sn−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 Wn,r = U(n)/U(n − r ), the matrix analogs of the double and coupled Neumann systems. |
dc.format.extent | 40 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject.lcsh | Geometry |
dc.title | Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability |
dc.type | Article |
dc.subject.lemac | Geometria diferencial |
dc.subject.lemac | Geodèsia matemàtica |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1007/s00209-010-0818-y |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::17 Nonassociative rings and algebras::17B Lie algebras and Lie superalgebras |
dc.subject.ams | Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry |
dc.subject.ams | Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
dc.relation.publisherversion | http://www.springerlink.com/content/c1j422973455433k/ |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 5402428 |
dc.description.version | Postprint (published version) |
local.citation.author | Fedorov, Y. |
local.citation.publicationName | Mathematische Zeitschrift |
local.citation.startingPage | 1 |
local.citation.endingPage | 40 |
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