Ricci Yang-Mills solitons on nilpotent Lie groups

Details Ricci Yang-Mills solitons on nilpotent Lie groups Ricci Yang-Mills solitons on nilpotent Lie groups

2009-07-07

arxiv.org/abs/0907.1095v2

Mathematics

Differential Geometry

14 pages; fixed a typo in Theorem 3.18

Scientific paper

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.

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