Regularity of infinitesimal automorphisms of involutive structures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913919599116288 |
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| author | Lamel, Bernhard Rodrigues, Nicholas Braun |
| author_facet | Lamel, Bernhard Rodrigues, Nicholas Braun |
| contents | In this paper, we prove that infinitesimal automorphisms of an involutive structure are smooth. For this, we build a regularity theory for sections of vector bundles over an involutive structure $(M,V)$ endowed with a connection compatible with $V$, which we call $V$-connection. We show that $V$-sections, i.e. sections which are parallel with respect to $V$ under the $V$-connection, satisfy an analogue of Hans Lewy's theorem as formulated for CR functions on an abstract CR manifold by Berhanu and Xiao, and introduce certain (generically satisfied) nondegeneracy conditions ensuring their smoothness. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_24105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity of infinitesimal automorphisms of involutive structures Lamel, Bernhard Rodrigues, Nicholas Braun Complex Variables 32V05, 35A30, 58A30 In this paper, we prove that infinitesimal automorphisms of an involutive structure are smooth. For this, we build a regularity theory for sections of vector bundles over an involutive structure $(M,V)$ endowed with a connection compatible with $V$, which we call $V$-connection. We show that $V$-sections, i.e. sections which are parallel with respect to $V$ under the $V$-connection, satisfy an analogue of Hans Lewy's theorem as formulated for CR functions on an abstract CR manifold by Berhanu and Xiao, and introduce certain (generically satisfied) nondegeneracy conditions ensuring their smoothness. |
| title | Regularity of infinitesimal automorphisms of involutive structures |
| topic | Complex Variables 32V05, 35A30, 58A30 |
| url | https://arxiv.org/abs/2506.24105 |