Examples for Cross Curvature Flow on 3-Manifolds

2004/05/14 by Li Ma, Ma, Li, Dezhong Chen +1
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0405275

14 pages

arxiv created 2004/05/14 · arxiv updated 2009/12/01

Abstract

Recently, B.Chow and R.S.Hamilton introduced the cross curvature flow on 3-manifolds. In this paper, we analyze two interesting examples for this new flow. One is on a square torus bundle over a circle, and the other is on a S² bundle over a circle. We show that the global flow exist in both cases. But on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity.

Related

• Cross Curvature Flow on Locally Homogenous Three-manifolds (I)
• Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
• Generalized cross curvature flow
• The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature
• Long Time Existence of the Cross Curvature Flow in 3-Manifolds with Negative Sectional Curvature