{
  "abstract": "In this article, we study Ricci-Yamabe solitons on the Lie group $\\mathrm{Sol} \\times \\mathbb{R}^n$ 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 $\\operatorname{Span}\\{\\partial_{t_1}, \\dots, \\partial_{t_n}\\}$, and we explicitly provide the Perelman potential.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12237",
  "author_total": 2,
  "authors": [
    {
      "name": "Abdou Bousso"
    },
    {
      "name": "Ameth Ndiaye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fze798q1vshc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12237",
  "fulltext_url": null,
  "id": "0fze798q1vshc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12237",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212841506",
  "pdf_url": "https://arxiv.org/pdf/2609.12237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fze798q1vshc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ricci-Yamabe solitons on the Lie group $\\Sol \\times \\mathbb{R}^n$",
  "title_text": "Ricci-Yamabe solitons on the Lie group Sol × ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/0fze798q1vshc",
  "venue": "arXiv",
  "versions": []
}