On strongly convex weakly Kähler–Finsler metrics of constant flag curvature

Abstract

In this study, we first provide a necessary and sufficient condition for a strongly convex weakly Kähler–Finsler metric to be of constant flag curvature, and we then prove that: (i) a strongly convex weakly Kähler–Finsler metric of constant flag curvature is necessarily of constant holomorphic curvature; and (ii) a strongly convex Kähler–Berwald metric on a complex manifold of complex dimension n≥2 has constant flag curvature if and only if it comes from a strongly convex locally complex Minkowski metric. We also give two examples of nontrivial strongly convex Kähler–Finsler metrics.