Contact Spheres and Hyperkähler Geometry

@article{Geiges2001ContactSA,
  title={Contact Spheres and Hyperk{\"a}hler Geometry},
  author={Hansjorg Geiges and Jes'us Gonzalo P'erez},
  journal={Communications in Mathematical Physics},
  year={2001},
  volume={287},
  pages={719-748}
}
  • H. Geiges, J. P'erez
  • Published 10 October 2001
  • Mathematics
  • Communications in Mathematical Physics
A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of taut contact spheres embeds into the moduli space of taut contact circles.This moduli problem leads to a new viewpoint on the Gibbons-Hawking ansatz in hyperkähler geometry. The… 
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