{
  "id": "1710.05361",
  "version": "v1",
  "published": "2017-10-15T16:54:15.000Z",
  "updated": "2017-10-15T16:54:15.000Z",
  "title": "A note on $λ$-convex set in complete Riemannian manifold",
  "authors": [
    "Absos Ali Shaikh",
    "Chandan Kumar Mondal",
    "Akhlad Iqbal"
  ],
  "comment": "6 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we have generalized the notion of $\\lambda$-radial contraction in complete Riemannian manifold and developed the concept of $p^\\lambda$-convex function. We have also given a counter example proving the fact that in general $\\lambda$-radial contraction of a geodesic is not necessarily a geodesic. We have also deduced some relation between geodesic convex set and $\\lambda$-convex set with respect to a point and show that under certain condition they are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-15T16:54:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A30",
      "52A42",
      "53B20",
      "53C20",
      "53C22"
    ],
    "keywords": [
      "complete riemannian manifold",
      "radial contraction",
      "geodesic convex set",
      "convex function",
      "counter example proving"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}