{
  "id": "2407.07212",
  "version": "v1",
  "published": "2024-07-09T20:08:48.000Z",
  "updated": "2024-07-09T20:08:48.000Z",
  "title": "Geometric inequalities for CR-submanifolds",
  "authors": [
    "Mirjana Djorić",
    "Vladimir Rovenski"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study two kinds of curvature invariants of Riemannian manifold equipped with a distribution (for example, a CR-submanifold of an almost Hermitian manifold) related to sets of pairwise orthogonal subspaces of the distribution: one is similar to Chen's $\\delta$-invariants and another kind of invariants is based on the mutual curvature of the subspaces. We compare Chen-type invariants with the mutual curvature invariants and prove geometric inequalities with intermediate mean curvature squared for CR-submanifolds in almost Hermitian spaces. In the case of a set of complex planes, we study curvature invariants based on the concept of holomorphic bisectional curvature. As applications, we give consequences of the absence of some $D$-minimal CR-submanifolds in almost Hermitian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T20:08:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric inequalities",
      "hermitian manifold",
      "holomorphic bisectional curvature",
      "study curvature invariants",
      "mutual curvature invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}