Homogeneous spaces, dynamics, cosmology: Geometric flows and rational dynamics
arXiv:1106.4720
Abstract
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to Bianchi-Ricci and Bianchi-Einstein flows, that is, the restricted finitely dimensional dynamical systems, obtained by considering homogeneous metrics.
Appeared in the Proceedings of the CIMPA school of El-Oued 2005te