K?hler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle

Let(M, g) be a compact K?hler manifold and(E, F) be a holomorphic Finsler vector bundle of rank r ≥ 2 over M. In this paper, we prove that there exists a K?hler metric Φ defined on the pro jective bundle P(E) of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for Φ having positive scalar curvature is obtained, and a sufficient condition for Φ having positive Ricci curvature is established.