Local and global structures on affine holomorphic bundles

Abstract

In this paper, we give some cohomological obstructions to the globalization of the holomorphic Liouville vector field, the totally singular complex Lagrangians, and the locally complex Lagrange structures defined on a local chart of an affine holomorphic bundle endowed with the natural holomorphic vertical foliation. We also consider the transversal distributions, we find the main obstructions to the globalization of a complex nonlinear connection and the existence of an affine transversal distribution.