中文摘要：

设（M，G）为n维复Finsler流形，TM为M的全纯切丛，得到了TM上的Hermite度量hTM=Gi-↑j（z,υ）dz^i×d-↑z^j＋Gi-↑j（z,υ）δυ^i×δ-↑υ^j为Kaehler度量的充要条件是M为全纯曲率为0的Kaehler流形，其中Gi-↑j=δ^2G/δυ^iδ-↑υ^j，1≤i，j≤n．推广了Cao-Wong的某些结果．

英文摘要：

Let （M, G） be a complex Finsler manifold of dimension n and TM its holomorphic tangent bundle. It is proved that the Hermitian metric hTM=Gi-↑j（z,υ）dz^i×d-↑z^j＋Gi-↑j（z,υ）δυ^i×δ-↑υ^j on TM is Kaehlerian if and only if （M, G） is a Kaehler manifold with zero holomorphic sectional curvature, where Gi-↑j=δ^2G/δυ^iδ-↑υ^j,1≤i,j≤n. It extends partially some results of Cao-Wong.