{
  "id": "1010.0956",
  "version": "v1",
  "published": "2010-10-05T17:45:28.000Z",
  "updated": "2010-10-05T17:45:28.000Z",
  "title": "Calabi product Lagrangian immersions in complex projective space and complex hyperbolic space",
  "authors": [
    "Haizhong Li",
    "Xianfeng Wang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Starting from two Lagrangian immersions and a Legendre curve $\\tilde{\\gamma}(t)$ in $\\mathbb{S}^3(1)$ (or in $\\mathbb{H}_1^3(1)$), it is possible to construct a new Lagrangian immersion in $\\mathbb{CP}^n$ (or in $\\mathbb{CH}^n$), which is called a warped product Lagrangian immersion. When $\\tilde{\\gamma}(t)=(r_1e^{i(\\frac{r_2}{r_1}at)}, r_2e^{i(- \\frac{r_1}{r_2}at)})$ (or $\\tilde{\\gamma}(t)=(r_1e^{i(\\frac{r_2}{r_1}at)}, r_2e^{i(\\frac{r_1}{r_2}at)})$), where $r_1$, $r_2$, and $a$ are positive constants with $r_1^2+r_2^2=1$ (or $-r_1^2+r_2^2=-1$), we call the new Lagrangian immersion a Calabi product Lagrangian immersion. In this paper, we study the inverse problem: how to determine from the properties of the second fundamental form whether a given Lagrangian immersion of $\\mathbb{CP}^n$ or $\\mathbb{CH}^n$ is a Calabi product Lagrangian immersion. When the Calabi product is minimal, or is Hamiltonian minimal, or has parallel second fundamental form, we give some further characterizations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-05T17:45:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B25",
      "53B20"
    ],
    "keywords": [
      "calabi product lagrangian immersion",
      "complex hyperbolic space",
      "complex projective space",
      "parallel second fundamental form",
      "warped product lagrangian immersion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.0956L"
    }
  }
}