Transversally holomorphic maps between Kähler foliations

We prove that any transversally holomorphic map between Kähler foliations is transversally harmonic with the minimum transversal fk-energy in its foliated homotopy class. Moreover, if either the transversal Ricci curvature of Kähler foliation F on M is non-negative and positive at some point or F is minimal, then any transversal Jacobi field of F is a transversally holomorphic field and conversely.