{
  "id": "math/0103220",
  "version": "v1",
  "published": "2001-03-30T12:42:09.000Z",
  "updated": "2001-03-30T12:42:09.000Z",
  "title": "Totally geodesic subgroups of diffeomorphisms",
  "authors": [
    "Stefan Haller",
    "Josef Teichmann",
    "Cornelia Vizman"
  ],
  "journal": "J. Geom. Phys. 42(2002), 342--354.",
  "doi": "10.1016/S0393-0440(01)00096-1",
  "categories": [
    "math.DG"
  ],
  "abstract": "We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant $L^2$-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of symplectic diffeomorphisms in the K\\\"ahler case. These are special cases of totally geodesic subgroups of diffeomorphisms with Lie algebras big enough to detect the vanishing of a symmetric 2-tensor field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-03-30T12:42:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D05",
      "58B20"
    ],
    "keywords": [
      "totally geodesic subgroup",
      "exact volume preserving diffeomorphisms",
      "lie algebras big",
      "considering right invariant",
      "riemannian manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}