Journal of Lie Theory 34 (2024), No. 2, 319--338
Copyright Heldermann Verlag 2024
Harmonic Vector Fields on 4-Dimensional Lorentzian Oscillator Groups
Zhiqi Chen
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, P. R. China
chenzhiqi@nankai.edu.cn
Bichao Sun
School of Microelectronics and Data Science, Anhui University of Technology, Maanshan, P. R. China
sbc15855629509@163.com
Ju Tan
School of Microelectronics and Data Science, Anhui University of Technology, Maanshan, P. R. China
tanju2007@163.com
We first give the Milnor-type theorem on the 4-dimensional Lorentzian oscillator group. Then we study harmonic sections and the critical point for the energy functional restricted to vector fields of the same length.
Keywords: Harmonic vector fields, harmonic sections, oscillator group.
MSC: 22E25, 53C30, 53C50.
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