Rigidity for Multi-Taub-NUT metrics

Details Rigidity for Multi-Taub-NUT metrics Rigidity for Multi-Taub-NUT metrics

2009-10-30

arxiv.org/abs/0910.5792v1

Mathematics

Differential Geometry

Scientific paper

This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperk\"ahler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard $\rl^3 \times \sph^1$ or a multi-Taub-NUT manifold. In particular, the underlying complex manifold is either $\cx \times \cx/\ir$ or a minimal resolution of a cyclic Kleinian singularity.

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