Examples for cross curvature flow on 3-manifolds

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. Mathematics Subject Classification (1991) 53C44