Open access
Author
Date
2014-08Type
- Journal Article
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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000088114Publication status
publishedExternal links
Journal / series
Monatshefte für MathematikVolume
Pages / Article No.
Publisher
SpringerSubject
Complex projective geometry; Cartan geometry; MetrisabilityOrganisational unit
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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