{
  "abstract": "‎‎This study focuses on identifying conditions that allow an $n$-dimensional compact Riemannian manifold $(M^n‎, ‎g)$ to support a vector field $\\xi$ along with smooth functions $\\alpha$ and $\\lambda$‎, forming an $(\\alpha,\\beta)$-Ricci--Yamabe soliton structure. Our construction relies on embedding $(M^n‎, ‎g)$ isometrically into the Euclidean space $(\\mathbb{R}^m‎, ‎g)$ following the method of Kuiper and Nash‎, ‎where $\\xi$ is defined as the tangential component of a fixed unit vector in $\\mathbb{R}^m$‎, ‎hereafter called the Kuiper-Nash vector‎. Let $r$ denote the scalar curvature of $(M^n‎, ‎g)$, ‎we establish that whenever the integral of $\\xi(r)$ satisfies a specific lower bound dependent on a constant $\\lambda$‎, ‎the tuple $(M^n‎, ‎g‎, ‎\\beta r‎, ‎\\xi‎, ‎\\lambda)$ forms a valid $(\\alpha,\\beta)$-Ricci-Yamabe soliton‎, ‎which we term a Kuiper-Nash $(\\alpha,\\beta)$-Ricci-Yamabe soliton‎. ‎We examine conditions under which the soliton becomes trivial‎, ‎presenting a characterization that directly relates this behavior to the scalar curvature r‎.‎Finally‎, ‎an explicit characterization is derived for a compact‎, ‎n-dimensional trivial Kuiper-Nash $(\\alpha,\\beta)$-Ricci-Yamabe soliton‎, ‎expressed in terms of an upper bound on the integral of $(\\mathrm{div}\\,\\xi)^2$ that incorporates r.",
  "abstract_shown": true,
  "affiliations": [
    "‎Department of Pure Mathematics‎, ‎‎Faculty of Science, Imam Khomeini International University, Qazvin‎, ‎I‎. ‎R‎. ‎Iran",
    "‎Department of Mathematics, ‎Payame Noor University, ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran",
    "‎Department of Mathematics‎, ‎ ‎Faculty of Mathematical Sciences and Statistics, ‎Malayer University, ‎Malayer‎, ‎I‎. ‎R‎. ‎Iran"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Shahroud azami"
    },
    {
      "affs": [
        1
      ],
      "name": "Mehdi Jafari"
    },
    {
      "affs": [
        2
      ],
      "name": "Mosayeb Zohrehvand"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2zv0815q7baa1.bib",
  "cited_by": 0,
  "doi": "10.22052/mir.2026.258097.1561",
  "fulltext_url": null,
  "id": "2zv0815q7baa1",
  "issns": [
    "2476-4965"
  ],
  "landing_url": "https://doi.org/10.22052/mir.2026.258097.1561",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7223695581",
  "pdf_url": "https://mir.kashanu.ac.ir/article_115848_e541ccdbfbfd41de68650c82bf63a37a.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "University of Kashan",
  "ris": "https://research.draconitic.com/paper/2zv0815q7baa1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:41Z",
      "native_id": "eb188721713b427889dd7d07e32c58b9",
      "source": "doaj",
      "url": "https://doi.org/10.22052/mir.2026.258097.1561"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "openalex:3103|Advanced Differential Geometry Research",
      "subfield": "general"
    }
  ],
  "title": "$(\\alpha,\\beta)$-Ricci-Yamabe Solitons with Potential Kuiper-Nash Vector Field",
  "title_text": "(α,β)-Ricci-Yamabe Solitons with Potential Kuiper-Nash Vector Field",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:41Z",
  "url": "https://research.draconitic.com/paper/2zv0815q7baa1",
  "venue": "Mathematics Interdisciplinary Research",
  "versions": []
}