POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES

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 in...

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Bibliographic Details
Published inNagoya mathematical journal Vol. 248; pp. 766 - 778
Main Author WU, KUANG-RU
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2022
Subjects
Mathematical functions
Norms
32J25
32L15
32F17
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0027-7630
2152-6842
DOI:10.1017/nmj.2022.2