{
  "abstract": "We study the iterated action of the Lie derivative on the curvature tensor of a Riemannian manifold with rank-one anisotropic curvature, whose Riemann tensor is expressed via the Kulkarni-Nomizu product as $R = λ(ξ^\\flat\\otimesξ^\\flat)\\owedge g$. First, we examine the conditions under which such a manifold admits a Ricci soliton structure and demonstrate that this property implies the almost $θ$-Yamabe soliton structure. Furthermore, we show that if the associated potential vector field $X$ is a symmetry of the Ricci tensor of a fixed order $k$ (i.e., $\\mathcal{L}_X^k \\operatorname{Ric} = 0$), the geometric problem reduces to solving a partial differential equation of order $k+1$ along the flow. Finally, under the assumption that $X$ is a conformal vector field ($\\mathcal{L}_X g = 2φg$) whose infinitesimal flow preserves the line distribution $\\mathcal{D}=\\operatorname{Span}\\{ξ\\}$ (with $[X,ξ]=aξ$ for $a\\in\\mathbb{R}$), we prove that several key geometric problems (such as establishing the relation $\\mathcal{L}_X^k R = R$, determining the minimal order $k$ for $X$ to be a Lie curvature symmetry, or satisfying $\\mathcal{L}_X^{k+1}R = f \\mathcal{L}_X^k R$ for a continuous function $f$) are equivalent to a scalar differential problem governed by the operator $D_X = X + 6φ+ 2a$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14866",
  "author_total": 2,
  "authors": [
    {
      "name": "Abdou Bousso"
    },
    {
      "name": "Ameth Ndiaye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jz0sa7r6kc59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14866",
  "fulltext_url": null,
  "id": "3jz0sa7r6kc59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14866",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7213297813",
  "pdf_url": "https://arxiv.org/pdf/2609.14866",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jz0sa7r6kc59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14866",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14866"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature",
  "title_text": "Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3jz0sa7r6kc59",
  "venue": "arXiv",
  "versions": []
}