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This paper has been withdrawn by the author some crucial errors