On complex Berwald metrics which are not conformal changes of complex Minkowski metrics
On complex Berwald metrics which are not conformal changes of complex Minkowski metrics
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DOI：
10.1515/advgeom-2017-0062
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发表时间：
2018-07
影响因子：
0.5
通讯作者：
Hongchuan Xia;Chunping Zhong
中科院分区：
文献类型：
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作者：
Hongchuan Xia;Chunping Zhong
摘要研究了整环D_n上的一类复Finsler度量.给出了这些度量是强伪凸复Finsler度量或复Berwald度量的充要条件。本文构造的复Berwald度量既不是平凡的Hermitian度量，也不是复Minkowski度量的共形变换。给出了具有迷向全纯曲率的复Berwald度量的一个刻划，也给出了这类复Finsler度量是Kähler Finsler度量或弱Kähler Finsler度量的刻划.此外，在强凸情形下，我们给出了这类复Finsler度量是射影平坦Finsler度量或对偶平坦Finsler度量的刻画.
Abstract We investigate a class of complex Finsler metrics on a domain D ⊂ ℂn. Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex Finsler metrics, or complex Berwald metrics, are given. The complex Berwald metrics constructed in this paper are neither trivial Hermitian metrics nor conformal changes of complex Minkowski metrics. We give a characterization of complex Berwald metrics which are of isotropic holomorphic curvatures, and also give characterizations of complex Finsler metrics of this class to be Kähler Finsler or weakly Kähler Finsler metrics. Moreover, in the strongly convex case, we give characterizations of complex Finsler metrics of this class to be projectively flat Finsler metrics or dually flat Finsler metrics.