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VOL. 48 | 2007 The Chern-Finsler connection and Finsler-Kähler manifolds

## Abstract

In this paper, we shall discuss the theory of connection in complex Finsler geometry, i.e., the Chern-Finsler connection $\nabla$ and its applications. In particular, we shall investigate (1) the ampleness of holomorphic vector bundles over a compact complex manifold which is based on the study due to [Ko1], (2) some special class of complex Finsler metrics and its characterization in terms of torsion and curvature of $\nabla$, and in the last section, (3) the characterization of Finsler-Kähler manifolds in terms of the Cartan connection $D$ which is naturally induced on the real tangent bundle from $\nabla$.

## Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1144.53030
MathSciNet: MR2389260

Digital Object Identifier: 10.2969/aspm/04810343