{
  "id": "math/0504010",
  "version": "v4",
  "published": "2005-04-01T07:16:31.000Z",
  "updated": "2008-03-01T06:46:15.000Z",
  "title": "Links between connections, parallel transports, and transports along paths in differentiable fibre bundles",
  "authors": [
    "Bozhidar Z. Iliev"
  ],
  "comment": "In v.4 is added a section devoted to some peculiarities of (parallel) transports in vector bundles. For other papers on this topic, view http://theo.inrne.bas.bg/~bozho/",
  "journal": "International Journal of Geometric Methods in Modern Physics, Vol. 2, No. 5 (2005) 823-838",
  "doi": "10.1142/S0219887805000806",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts \"connection\" and \"(axiomatically defined) parallel transport\" is established. Some results which are specific for topological and vector bundles are presented.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-03-01T06:46:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C99",
      "53C05",
      "55R99",
      "58A30"
    ],
    "keywords": [
      "differentiable fibre bundles",
      "connection",
      "parallel transport theory",
      "vector bundles",
      "axiomatic approach"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4010I"
    }
  }
}