复芬斯勒流形的全纯截面曲率
Holomorphic Sectional Curvature of Complex Finsler Manifolds.
作者信息
Wan Xueyuan
机构信息
Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden.
出版信息
J Geom Anal. 2019;29(1):194-216. doi: 10.1007/s12220-018-9985-6. Epub 2018 Jan 25.
Abstract
In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.
摘要
在本文中，我们得到了一个关于复芬斯勒度量的全纯截面曲率的不等式。作为应用，我们证明了从一个完备黎曼流形到一个复芬斯勒流形的施瓦茨引理。我们还表明，在一个额外条件下，具有半正但不恒为零的全纯截面曲率的强拟凸复芬斯勒流形具有负柯达依维数。
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