The collapsing geometry of almost Ricci-flat 4-manifolds
John Lott
University of California, Berkeley, USA
![The collapsing geometry of almost Ricci-flat 4-manifolds cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
We consider Riemannian 4-manifolds that Gromov–Hausdorff converge to a lower dimensional limit space, with the Ricci tensor going to zero. Among other things, we show that if the limit space is two dimensional then under some mild assumptions, the limiting four dimensional geometry away from the curvature blowup region is semiflat Kähler.
Cite this article
John Lott, The collapsing geometry of almost Ricci-flat 4-manifolds. Comment. Math. Helv. 95 (2020), no. 1, pp. 79–98
DOI 10.4171/CMH/481