Projectable Complex Nonlinear Connection and Complex Lagrange Foliations

Abstract

In this paper, we define the projectable complex nonlinear connection notion and we study some classes of foliations on a complex Lagrangian manifolds, which are related to the Lagrange metric extend to a bundle-like metric for the lifted foliation on the holomorphic tangent bundle. The notions are introduced in a similar manner to the real case[7], and the complex nonlinear connection considered is of the Cartan type.