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 G1(1).
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This research was supported by Youth Foundation of the Anhui University of Technology, Grant No. QZ201818, QZ201819, by NSFC, Grant No.11671212, 11771331 and by Natural Science Foundation of Anhui province, Grant No.1908085QA03.
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Xu, N., Tan, J. Invariant harmonic unit vector fields on the oscillator groups. Czech Math J 69, 907–924 (2019). https://doi.org/10.21136/CMJ.2019.0538-17
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DOI: https://doi.org/10.21136/CMJ.2019.0538-17