The Ricci Flow for Nilmanifolds
Differential Geometry
2008-12-12 v1 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.0812.2229,
title = {The Ricci Flow for Nilmanifolds},
author = {Tracy L. Payne},
journal= {arXiv preprint arXiv:0812.2229},
year = {2008}
}
Comments
28 pages