Rigidity for Multi-Taub-NUT metrics

Vincent Minerbe

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arXiv · 0910.5792

Rigidity for Multi-Taub-NUT metrics

Vincent Minerbe

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Abstract

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 $\rl^3 \times \sph^1$ 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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BibTeX RIS

Vincent Minerbe. 2009-10-30. Rigidity for Multi-Taub-NUT metrics. https://arxiv.org/abs/0910.5792

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