Displaying similar documents to “Pseudo-differential operators on V-manifolds and foliations (I).”

Lorentzian manifolds with special holonomy and parallel spinors

Leistner, Thomas

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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...