{
  "id": "2212.11928",
  "version": "v1",
  "published": "2022-12-22T18:03:39.000Z",
  "updated": "2022-12-22T18:03:39.000Z",
  "title": "The Gauss formula for the Laplacian on hypersurfaces",
  "authors": [
    "Chi Hin Chan",
    "Magdalena Czubak"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We extend the Gauss formula relating the extrinsic connection to the intrinsic connection to a formula for the extrinsic, Euclidean Laplacian to the intrinsic Laplacian of a vector field on a hypersurface. As a byproduct, we derive a formula for the Laplacian of a $1$-form on a surface of revolution in terms of the Lie derivatives. Physically, these formulas are motivated by the study of the formulation of the incompressible Navier-Stokes equations on a Riemannian manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-22T18:03:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypersurface",
      "intrinsic connection",
      "riemannian manifold",
      "intrinsic laplacian",
      "vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}