{
  "abstract": "This paper studies nontrivial Yamabe gradient solitons occurring as complete immersed hypersurfaces with constant scalar curvature in space forms $\\left(\\overline{M}^n(C), \\overline{g}\\right)$. For solitons with non-vanishing gradients, we establish a structural characterization of the soliton by analyzing a regular level set $Σ$ of the soliton function. In particular, imposing a suitable condition on the traceless part of the second fundamental form, $Φ^Σ_{\\overline{M}}$ of $Σ$ as a submanifold of the space form, we prove that the soliton either decomposes as a Riemannian product of $\\mathbb{R}$ and a totally umbilical submanifold of the space form, or satisfies a sharp lower bound on $\\sup\\limits_Σ\\left|Φ^Σ_{\\overline{M}}\\right|$. Furthermore, we show that the lower bound is attained if, and only if, the soliton is isometric to a Riemannian product of $\\mathbb{R}$ and a parallel submanifold of the space form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29298",
  "author_total": 2,
  "authors": [
    {
      "name": "Jahnabi Chakraborti"
    },
    {
      "name": "Anandateertha Mangasuli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnbc8d9jqtst8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29298",
  "fulltext_url": null,
  "id": "cnbc8d9jqtst8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29298",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7204875045",
  "pdf_url": "https://arxiv.org/pdf/2608.29298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnbc8d9jqtst8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Hypersurfaces of Space Forms That Are Gradient Yamabe Solitons",
  "title_text": "On Hypersurfaces of Space Forms That Are Gradient Yamabe Solitons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/cnbc8d9jqtst8",
  "venue": "arXiv",
  "versions": []
}