English

Complete Ricci flat Torus fibrations over ALE spaces

Differential Geometry 2014-03-11 v2

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.

Cite

@article{arxiv.1312.7404,
  title  = {Complete Ricci flat Torus fibrations over ALE spaces},
  author = {Kento Niikura},
  journal= {arXiv preprint arXiv:1312.7404},
  year   = {2014}
}

Comments

This paper has been withdrawn by the author some crucial errors

R2 v1 2026-06-22T02:36:05.970Z