{
  "id": "1010.2986",
  "version": "v2",
  "published": "2010-10-14T17:29:25.000Z",
  "updated": "2013-05-01T13:02:06.000Z",
  "title": "On the partial Ricci curvature of foliations",
  "authors": [
    "Vladimir Rovenski"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider a problem of prescribing the partial Ricci curvature on a locally conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal distributions $D_1$ and $D_2$. We provide conditions for symmetric $(0,2)$-tensors $T$ of a simple form (defined on $M$) to admit metrics $\\tilde g$, conformal to $g$, that solve the partial Ricci equations. The solutions are given explicitly. Using above solutions, we also give examples to the problem of prescribing the mixed scalar curvature related to $D_i$. In aim to find \"optimally placed\" distributions, we calculate the variations of the total mixed scalar curvature (where again the partial Ricci curvature plays a key role), and give examples concerning minimization of a total energy and bending of a distribution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-01T13:02:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C12"
    ],
    "keywords": [
      "foliations",
      "partial ricci curvature plays",
      "partial ricci equations",
      "total mixed scalar curvature",
      "complementary orthogonal distributions"
    ],
    "publication": {
      "doi": "10.1016/j.geomphys.2014.09.003",
      "journal": "Journal of Geometry and Physics",
      "year": 2014,
      "month": "Dec",
      "volume": 86,
      "pages": 370
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JGP....86..370R"
    }
  }
}