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Ricci-Yamabe solitons on the Lie group Sol × ℝn
Abstract
In this article, we study Ricci-Yamabe solitons on the Lie group Sol × ℝn equipped with a natural left-invariant Riemannian metric, explicitly determining the vector fields that characterize them. We then deduce that, in the case of a Ricci soliton, it is expanding, whereas in the case of a Yamabe soliton, it is shrinking. Finally, we show that if this Lie group is a gradient Ricci-Yamabe soliton, the vector field belongs to Span{∂t1, …, ∂tn}, and we explicitly provide the Perelman potential.
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BibTeX
@misc{bousso2026ricciyamabe,
title = {{Ricci-Yamabe solitons on the Lie group $\Sol \times \mathbbR^n$}},
author = {Abdou Bousso and Ameth Ndiaye},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12237},
eprint = {2609.12237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12237},
}
RIS
TY - UNPB
TI - Ricci-Yamabe solitons on the Lie group Sol × ℝ^n
AU - Abdou Bousso
AU - Ameth Ndiaye
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12237
UR - https://arxiv.org/abs/2609.12237
AB - In this article, we study Ricci-Yamabe solitons on the Lie group Sol × ℝ^n equipped with a natural left-invariant Riemannian metric, explicitly determining the vector fields that characterize them. We then deduce that, in the case of a Ricci soliton, it is expanding, whereas in the case of a Yamabe soliton, it is shrinking. Finally, we show that if this Lie group is a gradient Ricci-Yamabe soliton, the vector field belongs to Span{∂_t_1, …, ∂_t_n}, and we explicitly provide the Perelman potential.
ER -