Abstract
Kuranishi’s fundamental result (1962) associates to any compact complex manifold
{X_{0}}
a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to
{X_{0}}
. In this paper, we give an analogous statement for Levi-flat CR-manifolds fibering properly over the circle by associating to any such
{\mathcal{X}_{0}}
the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR-structures close to
{\mathcal{X}_{0}}
. We then develop in this context a Kodaira–Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.
Perturbation of a Class of CR Structures of Codimension Larger Than One
