Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 907-924, 2019
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
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: email@example.com, firstname.lastname@example.org