{
  "id": "1805.10088",
  "version": "v1",
  "published": "2018-05-25T11:41:46.000Z",
  "updated": "2018-05-25T11:41:46.000Z",
  "title": "Submanifolds with constant principal curvatures in Riemannian symmetric spaces",
  "authors": [
    "Jurgen Berndt",
    "Victor Sanmartin-Lopez"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds are always austere, hence minimal, and have constant principal curvatures. Well-known classes of examples include totally geodesic submanifolds, homogeneous austere hypersurfaces, and singular orbits of cohomogeneity one actions. The main purpose of this article is to present a systematic approach to the construction and classification of homogeneous submanifolds whose principal curvatures are independent of the normal direction in irreducible Riemannian symmetric spaces of non-compact type and rank greater than one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T11:41:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C35",
      "53C40"
    ],
    "keywords": [
      "constant principal curvatures",
      "normal direction",
      "irreducible riemannian symmetric spaces",
      "study submanifolds",
      "well-known classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}