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Harmonicity of vector fields on a class of Lorentzian solvable Lie groups
Tan Ju,Deng Shaoqiang * #
School of Mathematical Sciences, Nankai University, Tianjin 300071
*Correspondence author
#Submitted by
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Funding: SRFDP of China （No.20130031110005）
Opened online:12 May 2017
Accepted by: none
Citation: Tan Ju,Deng Shaoqiang.Harmonicity of vector fields on a class of Lorentzian solvable Lie groups[OL]. [12 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733161
 
 
In this paper, we consider a special class of solvable Lie groups such that for any $x, y$ in its Lie algebra, $[x, y]$ is a linear combination of $x$ and $y$. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.
Keywords:Solvable Lie groups; Lorenztian metrics; Harmonic vector fields
 
 
 

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