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POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES

Part of: Holomorphic fiber spaces Geometric convexity Compact analytic spaces

Published online by Cambridge University Press:  08 March 2022

KUANG-RU WU Open the ORCID record for KUANG-RU WU [Opens in a new window]
KUANG-RU WU*
Affiliation:
Institute of Mathematics Academia Sinica Taipei Taiwan krwu@gate.sinica.edu.tw
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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.

MSC classification

Primary: 32J25: Transcendental methods of algebraic geometry
Secondary: 32F17: Other notions of convexity 32L15: Bundle convexity

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Type
Article
Information
Nagoya Mathematical Journal , Volume 248 , December 2022 , pp. 766 - 778
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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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