Harmonicity and Existence of Algebraic Generalized Ricci Solitons

@misc{chen2026harmonicity,
  title = {{Harmonicity and Existence of Algebraic Generalized Ricci Solitons}},
  author = {Huibin Chen and Zhiqi Chen and Fuhai Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16029},
  eprint = {2609.16029},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16029},
}

TY  - UNPB
TI  - Harmonicity and Existence of Algebraic Generalized Ricci Solitons
AU  - Huibin Chen
AU  - Zhiqi Chen
AU  - Fuhai Zhu
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.16029
UR  - https://arxiv.org/abs/2609.16029
AB  - In this paper, we study the harmonicity and existence of algebraic generalized Ricci solitons. Firstly, we characterize harmonic torsion of algebraic generalized Ricci solitons on arbitrary metric Lie algebras by an identity involving the Killing form. In particular, positive semidefiniteness of the Killing form implies harmonicity without a unimodularity assumption. Then, we construct generalized nilsolitons with nonzero torsion on indecomposable three-step nilpotent Lie algebras admitting no classical nilsoliton, in dimension seven and in dimensions 6m+d for m>d≥1. Furthermore, we provide a spectral obstruction for nilpotent Lie algebras with abelian derived algebra and an obstruction based on the action of derivations on the quotient by the center. Combining these obstructions with explicit constructions, we prove that the filiform Lie algebra m_2(n), n≥5, admits a generalized nilsoliton if and only if 5≤ n≤8.
ER  -