Mathematical Research Letters
Volume 27 (2020)
Complex Finsler vector bundles with positive Kobayashi curvature
Pages: 1325 – 1339
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.
Huitao Feng was partially supported by NSFC(Grant No. 11221091, 11271062, 11571184, 11771070), the Fundamental Research Funds for the Central Universities and Nankai Zhide Foundation.
Kefeng Liu was partially supported by NSF (Grant No. 1510216).
Received 26 June 2019
Accepted 26 October 2019
Published 12 January 2021