复Einstein-Finsler双扭曲积度量

Complex Einstein-Finsler Doubly-warped Product Metric

设F是强拟凸的复Finsler度量F_1和F_2的双扭曲积.给出了F是复Einstein-Finsler度量的充分必要条件,并在F是一个广义复Einstein-Finsler度量的条件下,证明了它的全纯曲率恒为零.

Let F be a doubly warped product metric of strongly pseudo-convex complex Finsler metrics F1 and F2.In this paper,a necessary and sufficient condition for F to be a complex Einstein-Finsler metric is obtained.Under the condition that F is a generalized complex Einstein-Finsler metric,we prove that the holomorphic curvature of F vanishes identically.