Euler-like vector fields, normal forms, and isotropic embeddings
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916496841637888 |
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| author | Meinrenken, Eckhard |
| author_facet | Meinrenken, Eckhard |
| contents | Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric structures to the construction of an Euler-like vector field compatible with the given structure. We illustrate this principle in a variety of examples, including the Morse-Bott lemma, Weinstein's Lagrangian embedding theorem, and Zung's linearization theorem for proper Lie groupoids. In the second part of this article, we extend the theory to a weighted context, with an application to isotropic embeddings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2001_10518 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Euler-like vector fields, normal forms, and isotropic embeddings Meinrenken, Eckhard Differential Geometry Symplectic Geometry Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric structures to the construction of an Euler-like vector field compatible with the given structure. We illustrate this principle in a variety of examples, including the Morse-Bott lemma, Weinstein's Lagrangian embedding theorem, and Zung's linearization theorem for proper Lie groupoids. In the second part of this article, we extend the theory to a weighted context, with an application to isotropic embeddings. |
| title | Euler-like vector fields, normal forms, and isotropic embeddings |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2001.10518 |