Chern forms of holomorphic Finsler vector bundles and some applications

Huitao Feng Kefeng Liu Xueyuan Wan

Differential Geometry mathscidoc:1912.43079

International Journal of Mathematics, 27, (4), 1650030, 2016.4
In this paper, we present two kinds of total Chern forms c(E,G) and c(E,G) as well as a total Segre form c(E,G) of a holomorphic Finsler vector bundle c(E,G) expressed by the Finsler metric c(E,G), which answers a question of Faran [The equivalence problem for complex Finsler Hamiltonians, in <i>Finsler Geometry</i>, Contemporary Mathematics, Vol. 196 (American Mathematical Society, Providence, RI, 1996), pp. 133144] to some extent. As some applications, we show that the signed Segre forms c(E,G) are positive c(E,G)-forms on c(E,G) when c(E,G) is of positive Kobayashi curvature; we prove, under an extra assumption, that a FinslerEinstein vector bundle in the sense of Kobayashi is semi-stable; we introduce a new definition of a flat Finsler metric, which is weaker than Aikous one [Finsler geometry on complex vector bundles, in <i>A Sampler of RiemannFinsler Geometry</i>, MSRI Publications, Vol. 50 (Cambridge
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  title={Chern forms of holomorphic Finsler vector bundles and some applications},
  author={Huitao Feng, Kefeng Liu, and Xueyuan Wan},
  booktitle={International Journal of Mathematics},
Huitao Feng, Kefeng Liu, and Xueyuan Wan. Chern forms of holomorphic Finsler vector bundles and some applications. 2016. Vol. 27. In International Journal of Mathematics. pp.1650030.
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