Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)

Details Cross Curvature Flow on Locally Homogeneous Three-manifolds (II) Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)

2008-05-22

arxiv.org/abs/0805.3380v1

Mathematics

Differential Geometry

39 pages

Scientific paper

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.

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