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|Title:||On the classification of Lorentzian holonomy groups|
|Citation:||Journal of Differential Geometry, 2007; 76(3):423-484|
|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).|
|Appears in Collections:||Mathematical Sciences publications|
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