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Rigidity for Multi-Taub-NUT metrics

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 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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