Czechoslovak Mathematical Journal, first online, pp. 1-18


Invariant harmonic unit vector fields on the oscillator groups

Na Xu, Ju Tan

Received November 26, 2017.   Published online May 16, 2019.

Abstract:  We find all the left-invariant harmonic unit vector fields on the oscillator groups. Besides, we determine the associated harmonic maps from the oscillator group into its unit tangent bundle equipped with the associated Sasaki metric. Moreover, we investigate the stability and instability of harmonic unit vector fields on compact quotients of four dimensional oscillator group $G_1(1)$.
Keywords:  harmonic vector field; harmonic map; oscillator group
Classification MSC:  53C25, 53C43
DOI:  10.21136/CMJ.2019.0538-17

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Affiliations:   Na Xu, Ju Tan (corresponding author), School of Mathematics and Physics, Anhui University of Technology, Maxiang Road, Maanshan, Anhui Province, 243032, P. R. China e-mail: xuna406@163.com, tanju2007@163.com


 
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