Null Kähler Geometry and Isomonodromic Deformations
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Dunajski, M
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.
Description
Keywords
math.DG, math.DG, gr-qc, hep-th, nlin.SI
Journal Title
Communications in Mathematical Physics
Conference Name
Journal ISSN
0010-3616
1432-0916
1432-0916
Volume Title
391
Publisher
Springer Science and Business Media LLC