Positively curved Finsler metrics on vector bundles

2021/07/01 by Kuang-Ru Wu, Wu, Kuang-Ru · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Connective tissue disorders research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2107.00538

openalex publication_date 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²-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.

Cited by

• Uniform RC-positivity of direct image bundles
• Mean curvature of direct image bundles

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