Prolongation of Hermitian structures to J(2,0)M holomorphic jets bundle

Abstract

In the previous papers [14, 15], we made a study of the connections in the J^(2,0)M jet bundle. In the present paper, some results are applied in order to obtain adapted frames on J^(2,0)M for the prolongation of the Hermitian and complex Finsler structures on the base complex manifold M. Such prolongations are not in unique ways, but if (M, J_M, g) is a K¨ahler manifold, then there exists a unique nonlinear complex connection such that (J^(2,0)M, J, G) is the prolongation of the (M, J, g).