The Symplectic Normal Space of a Cotangent-Lifted Action

For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a sympl...

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Bibliographic Details
Published in:arXiv.org 2006-10
Main Authors: Perlmutter, Matthew, Rodriguez-Olmos, Miguel, Sousa-Dias, M Esmeralda
Format: Article
Language:English
Subjects:
Lie groups
Riemann manifold
Online Access:Get full text
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Summary:For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a symplectic linear space coming from reduction of a coadjoint orbit. This characterization of the symplectic normal space can be expressed solely in terms of the group action on the base manifold and the coadjoint representation. Some relevant particular cases are explored.
ISSN:2331-8422