Positively curved Finsler metrics on vector bundles III

Abstract

The goal of the paper is to extend results about ample or Griffiths positive vector bundles to Kobayashi positive vector bundles. In particular, we show that the quotient bundle of a Kobayashi positive vector bundle is Kobayashi positive, and the tensor product of two Kobayashi positive vector bundles is Kobayashi positive. These results strengthen the conjectural equivalences between ampleness, Griffiths positivity, and Kobayashi positivity. The proofs rely on the convexity of Kobayashi positive Finsler metrics and the duality for convex Finsler metrics.