Kähler Finsler Metrics and Conformal Deformations

Abstract: The conformal properties of complex Finsler metrics are studied. We give a characterization of a compact complex Finsler manifold to be globally conformal K\"ahler. The critical points of the total holomorphic curvature and total Ricci curvature in the volume preserved conformal classes are studied. The stability of critical K\"ahler Finsler metrics is obtained. A Yamabe type problem for mean Ricci curvature is considered.