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

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

2011-06-23

arxiv.org/abs/1106.4720v2

Geometries et Dynamiques, (2008) 275-305

Mathematics

Differential Geometry

Appeared in the Proceedings of the CIMPA school of El-Oued 2005te

Scientific paper

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.

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