Communications in Analysis and Geometry

Volume 17 (2009)

Number 2

Backward Ricci flow on locally homogeneous 3-manifolds

Pages: 305 – 325



Xiaodong Cao (Department of Mathematics, Cornell University)

Laurent Saloff-Coste (Department of Mathematics, Cornell University)


In this paper, we study the backward Ricci flow on locallyhomogeneous $3$-manifolds. We describe the long timebehavior and show that, typically and after a proper re-scaling,there is convergence to a sub-Riemannian geometry. A similarbehavior was observed by the authors in the case of the crosscurvature flow.

Published 1 January 2009