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PreprintCC BY-SA 4.0arXiv

Generalized Ricci Solitons on Heisenberg and Oscillator Algebras

  • Vicente Cortés
  • Shubham Dwivedi
  • Lorenz Jetter
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Abstract

We prove that on a connected, simply-connected nilpotent Lie group, the notions of left-invariant generalized Ricci soliton, semi-algebraic and algebraic generalized Ricci soliton coincide. Moreover, every such soliton has harmonic torsion. We classify all algebraic solitons with positive definite metric on the five-dimensional Heisenberg algebra, the four-dimensional oscillator algebra and the four-dimensional split-oscillator algebra up to automorphisms and rescalings. We find that there is only a finite number of algebraic solitons, all of which have harmonic torsion.

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Cite

BibTeXRIS
BibTeX
@misc{cortes2026generalized,
  title = {{Generalized Ricci Solitons on Heisenberg and Oscillator Algebras}},
  author = {Vicente Cortés and Shubham Dwivedi and Lorenz Jetter},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02062},
  eprint = {2611.02062},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02062},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Ricci Solitons on Heisenberg and Oscillator Algebras
AU  - Vicente Cortés
AU  - Shubham Dwivedi
AU  - Lorenz Jetter
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02062
UR  - https://arxiv.org/abs/2611.02062
AB  - We prove that on a connected, simply-connected nilpotent Lie group, the notions of left-invariant generalized Ricci soliton, semi-algebraic and algebraic generalized Ricci soliton coincide. Moreover, every such soliton has harmonic torsion. We classify all algebraic solitons with positive definite metric on the five-dimensional Heisenberg algebra, the four-dimensional oscillator algebra and the four-dimensional split-oscillator algebra up to automorphisms and rescalings. We find that there is only a finite number of algebraic solitons, all of which have harmonic torsion.
ER  -