Analysis reveals Riemann solitons in the oscillator group, suggesting implications for Ricci bi-conformal vector fields and their classifications.
We consider Riemann soliton vector fields and Ricci bi-conformal vector fields on the oscillator group. We prove that the oscillator group admits Riemann solitons. Subsequently, we provide a complete classification of all Ricci bi-conformal vector fields admitted by the oscillator group and identify those that belong to specific categories, namely gradient-type vector fields, Killing vector fields, and Ricci collineation using the partial differential equations.
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Chen et al. (2026) studied this question.
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