Mathematical Research Letters

Volume 27 (2020)

Number 5

Complex Finsler vector bundles with positive Kobayashi curvature

Pages: 1325 – 1339

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n5.a3

Authors

Huitao Feng (Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, China)

Kefeng Liu (Mathematical Science Research Center, Chongqing University of Technology, Chongqing, China; and Department of Mathematics, University of California, Los Angeles, Calif., U.S.A.)

Xueyuan Wan (School of Mathematics, Korea Institute for Advanced Study, Seoul, South Korea)

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.

Full Text (PDF format)

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