Ricci Yang-Mills solitons on nilpotent Lie groups
Differential Geometry
2012-10-23 v2
Abstract
The purpose of this paper is to introduce the Ricci Yang-Mills soliton equations on nilpotent Lie groups. In the 2-step nilpotent setting, we show that these equations are strictly weaker than the Ricci soliton equations. Using techniques from Geometric Invariant Theory, we develop a procedure to build many different kinds of Ricci Yang-Mills solitons. We finish this note by producing examples of Lie groups that do not admit Ricci soliton metrics but that do admit Ricci Yang-Mills soliton metrics.
Keywords
Cite
@article{arxiv.0907.1095,
title = {Ricci Yang-Mills solitons on nilpotent Lie groups},
author = {Michael Jablonski and Andrea Young},
journal= {arXiv preprint arXiv:0907.1095},
year = {2012}
}
Comments
14 pages; fixed a typo in Theorem 3.18