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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| Published in | Nagoya mathematical journal Vol. 248; pp. 766 - 778 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.12.2022
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| Subjects | |
| Online Access | Get full text |
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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. |
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| AbstractList | 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. 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. 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. |
| Author | WU, KUANG-RU |
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| Cites_doi | 10.4310/jdg/1536285628 10.1515/9781400858682 10.1215/ijm/1256044938 10.4007/annals.2015.181.3.6 10.4007/annals.2009.169.531 10.1017/S0027763000016615 10.24033/asens.2084 10.2969/jmsj/06841461 10.2140/pjm.1984.110.355 10.1007/s00208-016-1472-4 10.1017/S0027763000015919 10.4310/jdg/1236604342 10.1007/BF01446914 10.1090/S0002-9939-2015-12472-0 10.1090/conm/196/02440 10.1007/BF01421592 10.1090/S1056-3911-2012-00588-8 10.1142/S0129167X16500300 10.1090/conm/712/14346 |
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| Snippet | 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... 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... |
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| Title | POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES |
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