The Symplectic Normal Space of a Cotangent-Lifted Action
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2005
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| _version_ | 1866915106040840192 |
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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 |