Lax-type flows on grassmann manifolds and dual momentum mappings

A. K. Prykarpatsky; J. A. Zagrodziński; D. L. Blackmore

doi:10.1016/s0034-4877(97)85903-4

Lax-type flows on grassmann manifolds and dual momentum mappings

A. K. Prykarpatsky, J. A. Zagrodziński, D. L. Blackmore

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmann's procedure.

Original language	English (US)
Pages (from-to)	539-549
Number of pages	11
Journal	Reports on Mathematical Physics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/s0034-4877(97)85903-4
State	Published - Dec 1997

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1016/s0034-4877(97)85903-4

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title = "Lax-type flows on grassmann manifolds and dual momentum mappings",

abstract = "A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmann's procedure.",

author = "Prykarpatsky, {A. K.} and Zagrodzi{\'n}ski, {J. A.} and Blackmore, {D. L.}",

note = "Funding Information: One of the authors (A.P) would like to thank Prof. P. Winternitz and Prof. M. Haze-winkel for useful and interesting discussions during his stay at the Montreal University, Quebec, and at the Amsterdam University, the Netherlands. J.Z. acknowledges the support from the Polish Committee for Scientific Research (KBN), Grant 2P03B.114.11, and the support (A.P. & D.B.) from a NJIT Research Grant from Newark, NJ.",

year = "1997",

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doi = "10.1016/s0034-4877(97)85903-4",

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T1 - Lax-type flows on grassmann manifolds and dual momentum mappings

AU - Prykarpatsky, A. K.

AU - Zagrodziński, J. A.

AU - Blackmore, D. L.

N1 - Funding Information: One of the authors (A.P) would like to thank Prof. P. Winternitz and Prof. M. Haze-winkel for useful and interesting discussions during his stay at the Montreal University, Quebec, and at the Amsterdam University, the Netherlands. J.Z. acknowledges the support from the Polish Committee for Scientific Research (KBN), Grant 2P03B.114.11, and the support (A.P. & D.B.) from a NJIT Research Grant from Newark, NJ.

PY - 1997/12

Y1 - 1997/12

N2 - A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmann's procedure.

AB - A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmann's procedure.

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EP - 549

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

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Lax-type flows on grassmann manifolds and dual momentum mappings

Abstract

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