The Hamiltonian dynamics over real hypersurfaces in Kaehler manifolds

Abstract

Let X be a Kaehler manifold with complex dimension n. Let ω X be its Kaehler form. Let M be a strongly pseudo convex real hypersurface in X. For this hypersurface, the deformation theory of CR structures is successfully developed. And we find that H 1 ( M , T ′ ) (the T ′ -valued Kohn–Rossi cohomology) is the Zariski tangent space of the versal family. In this paper, the geometrical meaning of H 1 ( M , O ) is studied, and we propose to study displacements of the real hypersurface, which preserves the type of the differential form, ω X , over CR structures, on M, infinitesimally.