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Solvable Algebraic Generalized Ricci Solitons in low dimensions

  • Lorenzo Mucciante
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Abstract

We prove new structural results for algebraic generalized Ricci solitons on solvable Lie algebras and we discuss the existence of examples in low dimensions. We establish that all non-trivial solvable algebraic generalized Ricci solitons must be expanding and give necessary conditions for the existence of such solitons on one-dimensional extensions of abelian Lie algebras. Finally, we classify algebraic generalized Ricci solitons on three-dimensional Lie algebras, and algebraic generalized Ricci solitons on four-dimensional solvable unimodular Lie algebras, up to isometry and scaling.

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Cite

BibTeXRIS
BibTeX
@misc{mucciante2026solvable,
  title = {{Solvable Algebraic Generalized Ricci Solitons in low dimensions}},
  author = {Lorenzo Mucciante},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01608},
  eprint = {2610.01608},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01608},
}
RIS
TY  - UNPB
TI  - Solvable Algebraic Generalized Ricci Solitons in low dimensions
AU  - Lorenzo Mucciante
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01608
UR  - https://arxiv.org/abs/2610.01608
AB  - We prove new structural results for algebraic generalized Ricci solitons on solvable Lie algebras and we discuss the existence of examples in low dimensions. We establish that all non-trivial solvable algebraic generalized Ricci solitons must be expanding and give necessary conditions for the existence of such solitons on one-dimensional extensions of abelian Lie algebras. Finally, we classify algebraic generalized Ricci solitons on three-dimensional Lie algebras, and algebraic generalized Ricci solitons on four-dimensional solvable unimodular Lie algebras, up to isometry and scaling.
ER  -