{
  "id": "2505.02194",
  "version": "v1",
  "published": "2025-05-04T17:27:30.000Z",
  "updated": "2025-05-04T17:27:30.000Z",
  "title": "Biharmonic Curves in Warped Product Manifolds $I\\times_{f}M^{n}\\left( c\\right) $",
  "authors": [
    "Şaban Güvenç",
    "Cihan Özgür"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We explore the geometric properties of biharmonic curves in warped product manifolds of the form $I\\times _{f}M^{n}(c)$, where $I$ is an open interval and $M^{n}(c)$ is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct two examples in $I\\times _{f}S^{2}(1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-04T17:27:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C40",
      "53A04"
    ],
    "keywords": [
      "warped product manifolds",
      "biharmonic curves",
      "reveal deeper curvature-related characteristics",
      "constant curvature",
      "geometric properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}