Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/55223
Type: Journal article
Title: On the classification of Lorentzian holonomy groups
Author: Leistner, T.
Citation: Journal of Differential Geometry, 2007; 76(3):423-484
Publisher: Lehigh Univ
Issue Date: 2007
ISSN: 0022-040X
Statement of
Responsibility: 
Thomas Leistner
Abstract: If an (n + 2)-dimensional Lorentzian manifold is indecompos-able, but non-irreducible, then its holonomy algebra is contained in the parabolic algebra (R⊕so(n))⋉Rn. We show that its projec- tion 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).
RMID: 0020094460
Published version: http://www.intlpress.com/JDG/2007/JDG-v76.php
Appears in Collections:Mathematical Sciences publications

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