Weakly complex Einstein-Finsler vector bundle

Let (E, F) be a complex Finsler vector bundle over a compact Kahler manifold (M, g) with Kahler form I broken vertical bar. We prove that if (E, F) is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou (1997), then it is modeled on a complex Minkowski space. Consequently, a complex Einstein-Finsler vector bundle (E, F) over a compact Kahler manifold (M, g) is necessarily Phi-semistable and (E, F) = (E-1, F-1) circle plus...circle plus (E-1, F-1) where F-j := F vertical bar(Ej) , and each (E-j , F-j ) is modeled on a complex Minkowski space whose associated Hermitian vector bundle is a Phi-stable Einstein-Hermitian vector bundle with the same factor c as (E, F).