Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
复制标题
局部均匀三流形上的横曲率流动（II）
DOI：
10.4310/ajm.2009.v13.n4.a1
复制
发表时间：
2009
影响因子：
0.6
通讯作者：
L. Saloff‐Coste
中科院分区：
文献类型：
--
作者：
Xiaodong Cao;L. Saloff‐Coste
本文研究了局部齐次三维流形上的正交叉曲率流。我们描述了这些流量的长期行为。我们联合收割机将这一结果与先前关于负交叉曲率流的渐近行为的结果相结合，来描述局部齐次三维流形上交叉曲率流的极大解的双边行为。我们证明了局部齐次3-流形上的正交叉曲率流产生一个Heisenberg型次黎曼几何。
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.