{
  "id": "1308.0410",
  "version": "v2",
  "published": "2013-08-02T05:25:00.000Z",
  "updated": "2013-08-14T15:05:00.000Z",
  "title": "High-jet relations of the heat kernel embedding map and applications",
  "authors": [
    "Ke Zhu"
  ],
  "comment": "28 pages, related references on random functions are added",
  "categories": [
    "math.DG",
    "math.SP"
  ],
  "abstract": "For any compact Riemannian manifold $(M,g)$ and its heat kernel embedding map $psi_t$ from M into $l^2$ constructed in [BBG], we study the higher derivatives of $psi_t$ with respect to an orthonormal basis at $x$ on $M$. As the heat flow time $t$ goes to 0, it turns out the limiting angles between these derivative vectors are universal constants independent on $g$, $x$ and the choice of orthonormal basis. Geometric applications to the mean curvature and the Riemannian curvature are given. Some algebraic structures of the infinite jet space of $psi_t$ are explored.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-14T15:05:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "58J50"
    ],
    "keywords": [
      "heat kernel embedding map",
      "high-jet relations",
      "applications",
      "orthonormal basis",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0410Z"
    }
  }
}