复乘积流形上Berwald度量与强Khler-Finsler度量的构造(英文)

The Construction of Berwald Metrics and Strongly Khler-Finsler Metrics on Product Complex Manifolds

在一般的复乘积流形上构造了一类光滑的Finsler度量,证明了该度量是Berwald度量.得到了该度量的全纯曲率并在一定条件下证明了所构造的度量是强Kahler-Finsler度量.

In this paper, we construct a class of smooth complex Finsler metrics on some general product of complex manifolds and prove that these metrics are Berwald metrics. Furthermore, we get the holomorphic curvature of these metrics and prove that they are strongly Kahler-Finsler metrics under some conditions.