Null Kähler Geometry and Isomonodromic Deformations
Communications in Mathematical Physics
Springer Science and Business Media LLC
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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
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.
External DOI: https://doi.org/10.1007/s00220-021-04270-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334964