# American Institute of Mathematical Sciences

January  2010, 4(1): 65-90. doi: 10.3934/jmd.2010.4.65

## The Ricci flow for nilmanifolds

 1 Department of Mathematics, Idaho State University, 921 South 8th Ave., Stop 8085, Pocatello, ID 83209-8085, United States

Received  April 2009 Revised  October 2009 Published  May 2010

We consider the Ricci flow for simply connected nilmanifolds. This 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.
Citation: Tracy L. Payne. The Ricci flow for nilmanifolds. Journal of Modern Dynamics, 2010, 4 (1) : 65-90. doi: 10.3934/jmd.2010.4.65
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