Null Kähler Geometry and Isomonodromic Deformations
Authors
Dunajski, M
Publication Date
2022Journal Title
Communications in Mathematical Physics
ISSN
0010-3616
Publisher
Springer Science and Business Media LLC
Volume
391
Issue
1
Pages
77-105
Language
en
Type
Article
This Version
VoR
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Dunajski, M. (2022). Null Kähler Geometry and Isomonodromic Deformations. Communications in Mathematical Physics, 391 (1), 77-105. https://doi.org/10.1007/s00220-021-04270-0
Abstract
We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian
metrics admitting a compatible parallel nilpotent endomorphism of the tangent
bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in
the complexified setting) appear in the Bridgeland stability conditions of the
moduli spaces of Calabi-Yau three-folds.
Using twistor methods we show that, in dimension four - where there is a
connection with dispersionless integrability - the cohomogeneity-one
anti-self-dual null-K\"ahler metrics are generically characterised by solutions
to Painlev\'e I or Painlev\'e II ODEs.
Keywords
Article
Identifiers
s00220-021-04270-0, 4270
External DOI: https://doi.org/10.1007/s00220-021-04270-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334964
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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