Homogeneous spaces, dynamics, cosmology: Geometric flows and rational dynamics

Abdelghani Zeghib (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Abdelghani Zeghib. Homogeneous spaces, dynamics, cosmology: Geometric flows and rational dynamics. K. Saddalah and A. Zeghib. Geometries et Dynamiques, Hermann, pp.275-305, 2008, Travaux en cours 70. ⟨hal-00602656v2⟩