{
  "id": "1603.02803",
  "version": "v1",
  "published": "2016-03-09T08:03:03.000Z",
  "updated": "2016-03-09T08:03:03.000Z",
  "title": "A class of minimal submanifolds in spheres",
  "authors": [
    "Marcos Dajczer",
    "Theodoros Vlachos"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce a class of minimal submanfolds $M^n$, $n\\geq 3$, in spheres $\\mathbb{S}^{n+2}$ that are ruled by totally geodesic spheres of dimension $n-2$. If simply-connected, such a submanifold admits a one-parameter associated family of equally ruled minimal isometric deformations that are genuine. As for compact examples, there are plenty of them but only for dimensions $n=3$ and $n=4$. In the first case, we have that $M^3$ must be a $\\mathbb{S}^1$-bundle over a minimal torus $T^2$ in $\\mathbb{S}^5$ and in the second case $M^4$ has to be a $\\mathbb{S}^2$-bundle over a minimal sphere $\\mathbb{S}^2$ in $\\mathbb{S}^6$. In addition, we provide new examples in relation to the well-known Chern-do Carmo-Kobayashi problem since taking the torus $T^2$ to be flat yields a minimal submanifolds $M^3$ in $\\mathbb{S}^5$ with constant scalar curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-09T08:03:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal submanifolds",
      "well-known chern-do carmo-kobayashi problem",
      "equally ruled minimal isometric deformations",
      "constant scalar curvature",
      "compact examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160302803D"
    }
  }
}