Year: 2016
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Cintra, Adriana Araujo, Chen, Zhiqi, Neto, Benedito Leandro
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2509864784