{
  "id": "1110.1820",
  "version": "v1",
  "published": "2011-10-09T10:50:12.000Z",
  "updated": "2011-10-09T10:50:12.000Z",
  "title": "On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure",
  "authors": [
    "Dimitar Razpopov"
  ],
  "comment": "4 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \\in FM and (0, 1, 0, 0), respectively. Let \\nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_{4}, mu_{5}, mu_{6} be the sectional curvatures of 2-sections {x, qx}, {x, q^{2}x}, {q^{3}x, x}, {qx, q^{2}x}, {qx, q^{3}x}, {q^{2}x, q^{3}x} for arbitrary vector x in T_{p}M$, p is in M . Then we have that q^{4}=E; g(qx, qy)=g(x,y), x, y are in chiM. The main results of the present paper are 1) There exist a q-base in T_{p}M, p is in M. 2) if \\nabla q=0, then \\mu_{1}= \\mu_{3}=\\mu_{4}=\\mu_{6}, \\mu_{2}= \\mu_{5}=0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-09T10:50:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53B20"
    ],
    "keywords": [
      "dimensional riemannian manifold",
      "circulant affinor structure",
      "circulant metric",
      "arbitrary vector",
      "local coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1820R"
    }
  }
}