Complex Finsler vector bundles with positive Kobayashi curvature
Differential Geometry
2019-12-20 v3 Algebraic Geometry
Complex Variables
Abstract
In this short note, we prove that a complex Finsler vector bundle with positive Kobayashi curvature must be ample, which partially solves a problem of S. Kobayashi posed in 1975. As applications, a strongly pseudoconvex complex Finsler manifold with positive Kobayashi curvature must be biholomorphic to the complex projective space; we also show that all Schur polynomials are numerically positive for complex Finsler vector bundles with positive Kobayashi curvature.
Keywords
Cite
@article{arxiv.1811.08617,
title = {Complex Finsler vector bundles with positive Kobayashi curvature},
author = {Huitao Feng and Kefeng Liu and Xueyuan Wan},
journal= {arXiv preprint arXiv:1811.08617},
year = {2019}
}
Comments
10 pages. Minor changes, has accepted by Mathematical Research Letters