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HYPERKÄHLER STRUCTURES AND GROUP ACTIONS

  • ROGER BIELAWSKI (a1)

Abstract

A 4n-dimensional Riemannian manifold (M, g) is hyperkähler if it possesses three anti-commuting complex structures I, J, K such that the metric g is Kähler with respect to each of them. The reduced holonomy group of such a manifold is necessarily a subgroup of Sp(n) so the Ricci tensor of g vanishes and (M, g) can be regarded as a positive definite solution to Einstein's equations in vacuum.

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Corresponding author

Current address: Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, Bonn 53225, Germany. E-mail: rogerb@mpim-bonn.mpg.de

HYPERKÄHLER STRUCTURES AND GROUP ACTIONS

  • ROGER BIELAWSKI (a1)

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