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Title: Lorentzian manifolds with special holonomy and parallel spinors (English)
Author: Leistner, Thomas
Language: English
Journal: Proceedings of the 21st Winter School "Geometry and Physics"
Issue: 2001
Pages: [131]-159
Category: math
Summary: The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold -- a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian manifold and $\bbfR^n$, and gives examples starting with K\"ahler and hyper-K\"ahler manifolds. (English)
MSC: 53C27
MSC: 53C29
MSC: 53C50
idZBL: Zbl 1042.53033
idMR: MR1972431
Date available: 2009-07-13T21:47:27Z
Last updated: 2012-09-18
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