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Licensed Unlicensed Requires Authentication Published by De Gruyter March 1, 2011

Rigidity for Multi-Taub-NUT metrics

  • Vincent Minerbe EMAIL logo


This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperkähler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard or a Multi-Taub-NUT manifold. In particular, the underlying complex manifold is either ℂ × ℂ/ℤ or a minimal resolution of a cyclic Kleinian singularity.

Received: 2010-01-29
Revised: 2010-02-24
Published Online: 2011-03-01
Published in Print: 2011-July

© Walter de Gruyter Berlin · New York 2011

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