Folheações holomorfas tangentes a subconjuntos Levi-flat

Abstract

This thesis is devoted to the study of holomorphic foliations of dimension n, in local and global projective cases, which are tangent to Levi-at subsets. In this work, we will extend some aspects of the theory of Levi-at hypersurfaces invariant by holomorphic foliations to the context of Levi-at subsets. We study, in particular, in local and global cases, situations in which a foliation tangent to a Levi-at subset H has meromorphic or rational rst integral in the intrinsic complexicationH{. Finally, we study the integrability of special types of projective foliations tangent to Levi-at hypersurfaces, more specically foliations induced by closed 1-forms or with liouvillian rst integral or that are generic element of a linear pencil.