{
  "id": "1711.07928",
  "version": "v1",
  "published": "2017-11-21T17:24:47.000Z",
  "updated": "2017-11-21T17:24:47.000Z",
  "title": "Maslov, Chern-Weil and Mean Curvature",
  "authors": [
    "Tommaso Pacini"
  ],
  "comment": "10 pages, comments welcome",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "We provide an integral formula for the Maslov index of a pair $(E,F)$ over a surface $\\Sigma$, where $E\\rightarrow\\Sigma$ is a complex vector bundle and $F\\subset E_{|\\partial\\Sigma}$ is a totally real subbundle. As in Chern-Weil theory, this formula is written in terms of the curvature of $E$ plus a boundary contribution. When $(E,F)$ is obtained via an immersion of $(\\Sigma,\\partial\\Sigma)$ into a pair $(M,L)$ where $M$ is K\\\"ahler and $L$ is totally real, the boundary contribution is related to the mean curvature of $L$. In this context the formula thus allows us to control the Maslov index in terms of the geometry of $(M,L)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-21T17:24:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature",
      "maslov index",
      "boundary contribution",
      "complex vector bundle",
      "integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}