{
  "abstract": "We study Killing vector fields, Ricci solitons and hyperbolic Ricci solitons on the hyperbolic strip $S_a=\\{(x,y)\\in\\mathbb{R}^2:0<y<a\\}$ endowed with the metric $g_{S_{a}}=\\frac{π^2}{a^2\\sin^2(πy/a)}(dx^2+dy^2)$, and on its unit tangent bundle $T^1S_a$ endowed with the Sasaki metric $g^S$. On the strip, we show that the Gauss curvature is constant equal to $-1$, that the Lie algebra of Killing fields is isomorphic to $\\mathfrak{sl}(2,\\mathbb{R})$, that every Ricci soliton is trivial (Killing potential, $λ=-1$), and that a $2$-Killing field which is conformal, or which is the potential of a hyperbolic Ricci soliton with $λ\\neq0$, is a Killing field. On the unit tangent bundle, we prove that the Lie algebra of Killing fields of $(T^1S_a,g^S)$ is four-dimensional and isomorphic to $\\mathfrak{sl}(2,\\mathbb{R})\\oplus\\mathbb{R}$, that $g^S$ is not Einstein but is $η$-Einstein with constant coefficients, $\\operatorname{Ric}^S=-\\tfrac32\\,g^S+2\\,η\\otimesη$, and that $(T^1S_a,g^S)$ admits no Ricci soliton. For hyperbolic Ricci solitons we prove non-existence for Killing, left-invariant, and $θ$-invariant potentials with conformal projection, and we reduce the general $θ$-invariant case to a system of equations on the strip; the classification for an arbitrary potential is left open. Finally, we show that the $η$-Ricci solitons of $g^S$ have a Killing potential and $λ=\\tfrac32$, $μ=-2$, and that the $η$-hyperbolic Ricci solitons obtained in the same classes of potentials are the trivial ones, with a Killing potential, $μ=-\\tfrac32$ and $ν=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11705",
  "author_total": 3,
  "authors": [
    {
      "name": "Amadou Sy"
    },
    {
      "name": "Ameth Ndiaye"
    },
    {
      "name": "Ghodratallah Fasihi-Ramandi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3c189vz80pp91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11705",
  "fulltext_url": null,
  "id": "3c189vz80pp91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11705",
  "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": "W7221172908",
  "pdf_url": "https://arxiv.org/pdf/2610.11705",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3c189vz80pp91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11705",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11705"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$η-$ Hyperbolic Ricci Solitons on the Unit Tangent Bundle of the Hyperbolic Strip",
  "title_text": "η− Hyperbolic Ricci Solitons on the Unit Tangent Bundle of the Hyperbolic Strip",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3c189vz80pp91",
  "venue": "arXiv",
  "versions": []
}