Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$

Abstract

In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $\xi$ defined on a neighborhood of the closure of a bounded strongly convex open domain $\Omega \subset\mathbb C^n$ ($n\geq2$) with smooth boundary, with its boundary $\partial \Omega$. That is, any germ of deformation of $\mathcal{F}_0$ is also obtained by intersecting the orbits of a deformation of $\xi$ with the boundary of $\Omega$.