Affiliation:
1. Instytut Matematyki, Uniwersytet w Białymstoku, Ciołkowskiego 1M, 15–245 Białystok, Poland
Abstract
There are two groups which act in a natural way on the bundle [Formula: see text] tangent to the total space [Formula: see text] of a principal [Formula: see text]-bundle [Formula: see text]: the group [Formula: see text] of automorphisms of [Formula: see text] covering the identity map of [Formula: see text] and the group [Formula: see text] tangent to the structural group [Formula: see text]. Let [Formula: see text] be the subgroup of those automorphisms which commute with the action of [Formula: see text]. In the paper, we investigate [Formula: see text]-invariant symplectic structures on the cotangent bundle [Formula: see text] which are in a one-to-one correspondence with elements of [Formula: see text]. Since, as it is shown here, the connections on [Formula: see text] are in a one-to-one correspondence with elements of the normal subgroup [Formula: see text] of [Formula: see text], so the symplectic structures related to them are also investigated. The Marsden–Weinstein reduction procedure for these symplectic structures is discussed.
Publisher
World Scientific Pub Co Pte Lt
Subject
Mathematical Physics,Statistical and Nonlinear Physics