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POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES

Published online by Cambridge University Press:  08 March 2022

KUANG-RU WU*
Affiliation:
Institute of Mathematics Academia Sinica Taipei Taiwan krwu@gate.sinica.edu.tw

Abstract

We construct a convex and strongly pseudoconvex Kobayashi positive Finsler metric on a vector bundle E under the assumption that the symmetric power of the dual $S^kE^*$ has a Griffiths negative $L^2$ -metric for some k. The proof relies on the negativity of direct image bundles and the Minkowski inequality for norms. As a corollary, we show that given a strongly pseudoconvex Kobayashi positive Finsler metric, one can upgrade to a convex Finsler metric with the same property. We also give an extremal characterization of Kobayashi curvature for Finsler metrics.

Type
Article
Copyright
© (2022) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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