{
  "id": "1604.07346",
  "version": "v1",
  "published": "2016-04-21T21:27:12.000Z",
  "updated": "2016-04-21T21:27:12.000Z",
  "title": "A characterization of involutes and evolutes of a given curve in $\\mathbb{E}^{n}$",
  "authors": [
    "Günay Öztürk",
    "Kadri Arslan",
    "Betü Bulca"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "The orthogonal trajectories of the first tangents of the curve are called the involutes of $x$. The hyperspheres which have higher order contact with a curve $x$ are known osculating hyperspheres of $x$. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve $x$ in $n$-dimensional Euclidean space $\\mathbb{E}^{n}$. In the present study, we give a characterization of involute curves of order $k$ (resp. evolute curves) of the given curve $x$ in $n$-dimensional Euclidean space $\\mathbb{E}^{n}$. Further, we obtain some results on these type of curves in $\\mathbb{E}^{3}$ and $\\mathbb{E}^{4}$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-21T21:27:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional euclidean space",
      "characterization",
      "higher order contact",
      "involute curves",
      "osculating hyperspheres form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407346O"
    }
  }
}