  We first give a deformation theory of integrable distributions of codimension
1. We define a parametrization of families of smooth hypersurfaces near a Levi
flat hypersurface L such that the Levi flat deformations are given by the
solutions of the Maurer-Cartan equation in a DGLA associated to the Levi
foliation. We say that L is infinitesimally rigid if the tangent cone at the
origin to the moduli space of Levi flat deformations of L is trivial. We prove
the infinitesimal rigidity of compact transversally parallelisable Levi flat
hypersurfaces in compact complex manifolds and give sufficient conditions for
infinitesimal rigidity in Kahler manifolds. As an application, we prove the
nonexistence of transversally parallelizable Levi flat hypersurfaces in a class
of manifolds which contains the complex projective plane.
