Geometry of infinite dimensional Cartan Developments
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929454905819136 |
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| author | Michor, Johanna Michor, Peter W. |
| author_facet | Michor, Johanna Michor, Peter W. |
| contents | The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$ for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of infinite dimensional Cartan Developments Michor, Johanna Michor, Peter W. Differential Geometry Functional Analysis 58B25 The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$ for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development. |
| title | Geometry of infinite dimensional Cartan Developments |
| topic | Differential Geometry Functional Analysis 58B25 |
| url | https://arxiv.org/abs/2404.05416 |