Abstract
Let F be a doubly twisted product metric of two strongly pseudoconvex complex Finsler metrics F1 and F2. In this paper, we obtain a necessary and sufficient condition that F to be a complex Einstein-Finsler metric, and get the conclusion that F is a complex Einstein-Finsler metric if and only if F1 and F2 are weakly Einstein-Finsler metrics when logarithm functions of twisted functions both are pluriharmonic functions. We also proved that the holomorphic curvature of F vanishes identically under the condition that F is a complex generalized Einstein-Finsler metric.
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