Regularity of infinitesimal automorphisms of involutive structures

Bernhard Lamel; Nicholas Braun Rodrigues

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arXiv · 2506.24105

Regularity of infinitesimal automorphisms of involutive structures

Bernhard Lamel·Nicholas Braun Rodrigues

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Abstract

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.

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BibTeX RIS

Bernhard Lamel, Nicholas Braun Rodrigues. 2025-06-30. Regularity of infinitesimal automorphisms of involutive structures. https://arxiv.org/abs/2506.24105

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