{
  "id": "0807.1601",
  "version": "v4",
  "published": "2008-07-10T09:19:54.000Z",
  "updated": "2013-12-09T08:32:25.000Z",
  "title": "The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry",
  "authors": [
    "Naoyuki Koike"
  ],
  "comment": "25pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we first define the complexification of a real analytic map between real analytic Koszul manifolds and show that the complexified map is the holomorphic extension of the original map. Next we define an anti-Kaehler metric compatible with the adapted complex structure on the complexification of a real analytic pseudo-Riemannian manifold. In particular, for a pseudo-Riemannian homogeneous space, we define another complexification and a (complete) anti-Kaehler metric on the complexification. One of main purposes of this paper is to find the interesting relation between these two complexifications (equipped with the anti-Kaehler metrics) of a pseudo-Riemannian homogeneous space. Another of main purposes of this paper is to show that almost all principal orbits of some isometric action on the first complexification (equipped with the anti-Kaehler metric) of a semi-simple pseudo-Riemannian symmetric space are curvature-adapted isoparametric submanifolds with flat section in the sense of this paper.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-09T08:32:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C56",
      "53C42"
    ],
    "keywords": [
      "complexification",
      "anti-kaehler geometry",
      "anti-kaehler metric",
      "pseudo-riemannian homogeneous space",
      "real analytic pseudo-riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1601K"
    }
  }
}