The Ricci Flow for Nilmanifolds

Details The Ricci Flow for Nilmanifolds The Ricci Flow for Nilmanifolds

2008-12-11

arxiv.org/abs/0812.2229v1

Mathematics

Differential Geometry

28 pages

Scientific paper

We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product and the evolution of structure constants, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.'s for some of these flows and describe their qualitative properties. We also present some explicit solutions for the evolution of soliton metrics under the Ricci flow.

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