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Abstract: In this paper, we study the positive cross curvature flow on locallyhomogeneous 3-manifolds. We describe the long time behavior of these flows. Wecombine this with earlier results concerning the asymptotic behavior of thenegative cross curvature flow to describe the two sided behavior of maximalsolutions of the cross curvature flow on locally homogeneous 3-manifolds. Weshow that, typically, the positive cross curvature flow on locally homogeneous3-manifold produce an Heisenberg type sub-Riemannian geometry.



Author: Xiaodong Cao, Laurent Saloff-Coste

Source: https://arxiv.org/







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