{
  "id": "math/9910052",
  "version": "v3",
  "published": "1999-10-09T05:24:01.000Z",
  "updated": "2000-01-09T11:22:50.000Z",
  "title": "Submanifold Differential Operators in $\\Cal D$-Module Theory II: Generalized Weierstrass and Frenet-Serret Relations as Dirac Equations",
  "authors": [
    "Shigeki Matsutani"
  ],
  "comment": "AMS-Tex Use 22 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\\EE^n$ to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely represent the submanifolds. For example, the analytic index of Dirac operator of a space curve is identified with its writhing number. As another example, the operator determinants of the Dirac operators are closely related to invariances of the immersed objects, such as Euler-Bernoulli and Willmore functionals for a space curve and a conformal surface respectively. In this article, we will give mathematical construction of the Dirac operator by means of $\\Cal D$-module and reformulate my recent results mathematically.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-01-09T11:22:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac operator",
      "submanifold differential operators",
      "frenet-serret relation",
      "generalized weierstrass",
      "module theory"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....10052M"
    }
  }
}