Conformal vector fields on Lie groups
Differential Geometry
2016-09-30 v2
Abstract
In this paper, we investigated the behavior of left-invariant conformal vector fields on Lie groups with left-invariant pseudo-Riemannian metrics. First of all, we prove that conformal vector fields on pseudo-Riemannian unimodular Lie groups are Killing. Then we obtain a necessary condition for a pseudo-Rimennian non-unimodular Lie group admitting a non-Killing conformal vector field. Finally, we give examples of non-Killing conformal vector fields and Yamabe solitons on non-unimodular Lorentzian Lie groups based on the above study.
Keywords
Cite
@article{arxiv.1608.05943,
title = {Conformal vector fields on Lie groups},
author = {Adriana Araujo Cintra and Zhiqi Chen and Benedito Leandro Neto},
journal= {arXiv preprint arXiv:1608.05943},
year = {2016}
}