Asian Journal of Mathematics
Volume 13 (2009)
Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
Pages: 421 – 458
In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier results concerning the asymptotic behavior of the negative cross curvature flow to describe the two sided behavior of maximal solutions of the cross curvature flow on locally homogeneous 3-manifolds. We show that, typically, the positive cross curvature flow on locally homogeneous 3-manifold produce an Heisenberg type sub-Riemannian geometry.
Cross Curvature Flow (XCF); locally homogeneous 3-manifold
2010 Mathematics Subject Classification
Primary 53C44. Secondary 58J35.