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arXiv · 2010.11216

Null Kähler geometry and isomonodromic deformations

Maciej Dunajski
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Abstract

We construct the normal forms of null-Kähler 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-Kähler metrics are generically characterised by solutions to Painlevé I or Painlevé II ODEs.

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BibTeXRIS

Maciej Dunajski. 2021-11-11. Null Kähler geometry and isomonodromic deformations. https://doi.org/10.1007/s00220-021-04270-0

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