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Keywords:
harmonic vector field; harmonic map; oscillator group
harmonic vector field; harmonic map; oscillator group
Summary:
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 $G_1(1)$.
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