Examples for cross curvature flow on 3-manifolds

Original Article

DOI: 10.1007/s00526-005-0366-1

Cite this article as:
Ma, L. & Chen, D. Calc. Var. (2006) 26: 227. doi:10.1007/s00526-005-0366-1


Recently, B. Chow and R.S. Hamilton [3] 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 exists in both cases. However, on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity.


Cross curvature flowSquare torus bundleS2 bundle

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua universityBeijingChina