Conformal vector fields on Lie groups

Adriana Araujo Cintra; Zhiqi Chen; Benedito Leandro Neto

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arXiv · 1608.05943

Conformal vector fields on Lie groups

Adriana Araujo Cintra·Zhiqi Chen·Benedito Leandro Neto

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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.

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BibTeX RIS

Adriana Araujo Cintra, Zhiqi Chen, Benedito Leandro Neto. 2016-08-21. Conformal vector fields on Lie groups. https://arxiv.org/abs/1608.05943

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