On Kahler metrisability of two-dimensional complex projective structures
dc.contributor.author
Mettler, Thomas
dc.date.accessioned
2021-05-26T08:52:13Z
dc.date.available
2017-06-11T11:57:11Z
dc.date.available
2021-05-21T12:09:35Z
dc.date.available
2021-05-26T08:52:13Z
dc.date.issued
2014-08
dc.identifier.issn
0026-9255
dc.identifier.issn
1436-5081
dc.identifier.other
10.1007/s00605-014-0636-0
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/88114
dc.identifier.doi
10.3929/ethz-b-000088114
dc.description.abstract
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)Kähler metric. Furthermore we show that the (pseudo-)Kähler metrics defined on some domain in the projective plane which are compatible with the standard complex projective structure are in one-to-one correspondence with the hermitian forms on C3 whose rank is at least two. This is achieved by prolonging the relevant finite-type first order linear differential system to closed form. Along the way we derive the complex projective Weyl and Liouville curvature using the language of Cartan geometries.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Complex projective geometry
en_US
dc.subject
Cartan geometry
en_US
dc.subject
Metrisability
en_US
dc.title
On Kahler metrisability of two-dimensional complex projective structures
en_US
dc.type
Journal Article
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2014-05-27
ethz.journal.title
Monatshefte für Mathematik
ethz.journal.volume
174
en_US
ethz.journal.issue
4
en_US
ethz.pages.start
599
en_US
ethz.pages.end
616
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Wien
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
ethz.date.deposited
2017-06-11T11:57:45Z
ethz.source
ECIT
ethz.identifier.importid
imp59365234f11d480107
ethz.ecitpid
pub:138705
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-12T17:42:09Z
ethz.rosetta.lastUpdated
2022-03-29T08:11:51Z
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true
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