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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 486
Lorentzian manifolds with special holonomy and parallel spinors Thomas Leistner
We investigate the holonomy group of a simply connected, indecomposable and reducible Lorentzian spin manifold and the property that it should admit parallel spinors. We give a condition for such a holonomy to be abeleen, show that such manifolds with abeleen holonomy to be pp-manifolds and get as a consequence that pp-manifolds are the only Lorentzian manifolds with nontrivial abeleen holonomy and parallel spinors.
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