The Symplectic Normal Space of a Cotangent-Lifted Action

Fuente: arXiv
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Hauptverfasser: Perlmutter, Matthew, Rodriguez-Olmos, Miguel, Sousa-Dias, M. Esmeralda
Format: Preprint
Veröffentlicht: 2005
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author Perlmutter, Matthew
Rodriguez-Olmos, Miguel
Sousa-Dias, M. Esmeralda
author_facet Perlmutter, Matthew
Rodriguez-Olmos, Miguel
Sousa-Dias, M. Esmeralda
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_math_0501207
institution arXiv
publishDate 2005
record_format arxiv
spellingShingle The Symplectic Normal Space of a Cotangent-Lifted Action
Perlmutter, Matthew
Rodriguez-Olmos, Miguel
Sousa-Dias, M. Esmeralda
Symplectic Geometry
53D20, 70H14, 70H33
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.
title The Symplectic Normal Space of a Cotangent-Lifted Action
topic Symplectic Geometry
53D20, 70H14, 70H33
url https://arxiv.org/abs/math/0501207