关于可积结构的无穷小自同构的正则性

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。