Communications in Mathematical Physics

, Volume 108, Issue 4, pp 535–589 | Cite as

Hyperkähler metrics and supersymmetry

  • N. J. Hitchin
  • A. Karlhede
  • U. Lindström
  • M. Roček


We describe two constructions of hyperkähler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.


Neural Network Manifold Statistical Physic Complex System General Setting 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • N. J. Hitchin
    • 1
  • A. Karlhede
    • 2
  • U. Lindström
    • 2
  • M. Roček
    • 3
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUnited Kingdom
  2. 2.Institute of Theoretical PhysicsUniversity of StockholmStockholmSweden
  3. 3.Institute for Theoretical PhysicsState University of New YorkStony BrookUSA

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