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Holomorphic Vanishing Theorems on Finsler Holomorphic Vector Bundles and Complex Finsler Manifolds

Part of: Partial differential equations on manifolds; differential operators Global differential geometry

Published online by Cambridge University Press:  09 November 2018

Bin Shen
Bin Shen*
Affiliation:
School of Mathematics, Southeast University, 211189, Nanjing, P. R. China Email: [email protected]
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Abstract

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In this paper, we investigate the holomorphic sections of holomorphic Finsler bundles over both compact and non-compact complete complex manifolds. We also inquire into the holomorphic vector fields on compact and non-compact complete complex Finsler manifolds. We get vanishing theorems in each case according to different certain curvature conditions. This work can be considered as generalizations of the classical results on Kähler manifolds and hermitian bundles.

Keywords

complex Finsler metricholomorphic vector fieldholomorphic sectionG-average Ricci curvaturevanishing theorem

MSC classification

Primary: 53C60: Finsler spaces and generalizations (areal metrics)
Secondary: 53C56: Other complex differential geometry 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 623 - 641
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The author is supported by the Natural Science Foundation of Jiangsu Province (No. BK20160661) and Zhishan young Scholar Program of SEU (No. 2242019R40055).

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