Volume 21, issue 5 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
The nonuniqueness of the tangent cones at infinity of Ricci-flat manifolds

Kota Hattori

Geometry & Topology 21 (2017) 2683–2723
Abstract

Colding and Minicozzi established the uniqueness of the tangent cones at infinity of Ricci-flat manifolds with Euclidean volume growth where at least one tangent cone at infinity has a smooth cross section. In this paper, we raise an example of a Ricci-flat manifold implying that the assumption for the volume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifold of dimension $4$ with non-Euclidean volume growth that has infinitely many tangent cones at infinity where one of them has a smooth cross section.

Keywords
hyper-Kähler, tangent cone at infinity, Ricci flat manifold
Primary: 53C23