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4 May 2001 Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds
Sergey Pekarsky, Jerrold E. Marsden
J. Appl. Math. 1(1): 1-28 (4 May 2001). DOI: 10.1155/S1110757X01000043


When the phase space P of a Hamiltonian G-system (P,ω,G,J,H) has an almost Kähler structure a preferred connection, called abstract mechanical connection, can be defined by declaring horizontal spaces at each point to be metric orthogonal to the tangent to the group orbit. Explicit formulas for the corresponding connection one-form 𝒜 are derived in terms of the momentum map, symplectic and complex structures. Such connection can play the role of the reconstruction connection (due to the work of A. Blaom), thus significantly simplifying computations of the corresponding dynamic and geometric phases for an Abelian group G. These ideas are illustrated using the example of the resonant three-wave interaction. Explicit formulas for the connection one-form and the phases are given together with some new results on the symmetry reduction of the Poisson structure.


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Sergey Pekarsky. Jerrold E. Marsden. "Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds." J. Appl. Math. 1 (1) 1 - 28, 4 May 2001.


Published: 4 May 2001
First available in Project Euclid: 24 March 2003

zbMATH: 0998.53055
MathSciNet: MR1844945
Digital Object Identifier: 10.1155/S1110757X01000043

Primary: 37J15 , 53D20
Secondary: 32Q15

Rights: Copyright © 2001 Hindawi

Vol.1 • No. 1 • 4 May 2001
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