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arXiv · 1811.08617

Complex Finsler vector bundles with positive Kobayashi curvature

Huitao Feng·Kefeng Liu·Xueyuan Wan
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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.

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Huitao Feng, Kefeng Liu, Xueyuan Wan. 2019-12-19. Complex Finsler vector bundles with positive Kobayashi curvature. https://arxiv.org/abs/1811.08617

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