Abstract

Chow and Hamilton introduced the cross curvature flows on closed three-manifolds with negative or positive sectional curvature. We study the negative cross curvature flow in the case of locally homogeneous metrics on three-manifolds. In each case, we describe the long time behavior of the solutions of the corresponding ODE system.

Keywords

cross curvature flow, locally homogeneous three-manifolds

Mathematical Subject Classification

Primary: 53C44

Secondary: 58J35

Authors