Le théorème de l'indice relatif
Let , let be a hypersurface of , be a submanifold of . Denote by the Levi form of at . In a previous paper [3] two numbers , are defined; for they are the numbers of positive and negative eigenvalues for . For , , we show here that are still the numbers of positive and negative eigenvalues for when restricted to . Applications to the concentration in degree for microfunctions at the boundary are given.
In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds of , in particular Levi flat ones. As a general scheme, we suppose that is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.