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Null Kahler geometry and isomonodromic deformations

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 نشر من قبل Maciej Dunajski
 تاريخ النشر 2020
  مجال البحث فيزياء
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 تأليف Maciej Dunajski




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



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