Backward Ricci Flow on Locally Homogeneous 4-Manifolds

2015/07/31 by Thomas Bell, Thomas A. Bell, Bell, Thomas
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.1507.08988

arxiv created 2015/07/31 · arxiv updated 2015/08/03

Abstract

In this paper we study backward Ricci flow of locally homogeneous geometries of 4-manifolds which admit compact quotients. We describe the long-term behavior of each class and show that many of the classes exhibit the same behavior near the singular time. In most cases, these manifolds converge to a sub-Riemannian geometry after suitable rescaling.

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