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Advances in Geometry

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On complex Berwald metrics which are not conformal changes of complex Minkowski metrics

Hongchuan Xia / Chunping Zhong
Published Online: 2018-04-05 | DOI: https://doi.org/10.1515/advgeom-2017-0062

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.

Keywords: Complex Finsler metric; complex Berwald metric; holomorphic curvature

MSC 2010: 53C60; 53C40

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About the article


Received: 2015-01-17

Revised: 2016-07-01

Published Online: 2018-04-05


Funding: This work is supported by the National Natural Science Foundation of China (Grant Nos. 11671330, 11701494, 11571288, 11771357), the Nanhu Scholars Program for Young Scholars of XYNU, and the Scientific Research Fund Program for Young Scholars of XYNU (No. 2017-QN-029).


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0062.

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