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On the classification of lorentzian holonomy groups

Thomas Leistner Humboldt-Universit¨at Berlin

Differential Geometry mathscidoc:1609.10027

Journal of Differential Geometry, 76, (3), 423-484, 2007
If an (n + 2)-dimensional Lorentzian manifold is indecomposable, but non-irreducible, then its holonomy algebra is contained in the parabolic algebra (R⊕so(n)).Rn. We show that its projection onto so(n) is the holonomy algebra of a Riemannian manifold. This leads to a classification of Lorentzian holonomy groups and implies that the holonomy group of an indecomposable Lorentzian spin manifold with parallel spinor equals to G . Rn where G is a product of SU(p), Sp(q), G2 or Spin(7).
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@inproceedings{thomas2007on,
  title={ON THE CLASSIFICATION OF LORENTZIAN HOLONOMY GROUPS},
  author={Thomas Leistner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908202918006796684},
  booktitle={Journal of Differential Geometry},
  volume={76},
  number={3},
  pages={423-484},
  year={2007},
}
Thomas Leistner. ON THE CLASSIFICATION OF LORENTZIAN HOLONOMY GROUPS. 2007. Vol. 76. In Journal of Differential Geometry. pp.423-484. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908202918006796684.
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