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arXiv · 1312.7404

Complete Ricci flat Torus fibrations over ALE spaces

Kento Niikura
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Abstract

We investigate complete noncompact Ricci-flat manifolds which are not of maximal volume growth. We show that the manifolds with a curvature decay condition and a holonomy decay condition are asymptotic to torus fibrations over ALE spaces. In particular, we classify complete noncompact 4-dimensional hyperk\"aler manifolds by the volume growth. As an application, we give the uniqueness of tangent cones of collapsing manifolds with some conditions.

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Kento Niikura. 2013-12-28. Complete Ricci flat Torus fibrations over ALE spaces. https://arxiv.org/abs/1312.7404

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