Journal of Modern Dynamics (JMD)

The Ricci flow for nilmanifolds

Pages: 65 - 90, Issue 1, January 2010      doi:10.3934/jmd.2010.4.65

       Abstract        Full Text (296.6K)       Related Articles

Tracy L. Payne - Department of Mathematics, Idaho State University, 921 South 8th Ave., Stop 8085, Pocatello, ID 83209-8085, United States (email)

Abstract: 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.

Keywords:  nilmanifold, Ricci flow, soliton metric.
Mathematics Subject Classification:  Primary: 53C44; Secondary: 22E25.

Received: April 2009;      Revised: October 2009;      Available Online: May 2010.