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Local and global aspects of separating coordinates for the Klein-Gordon equation

Hinterleitner, Franz (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

The author considers the Klein-Gordon equation for ( 1 + 1 ) -dimensional flat spacetime. He is interested in those coordinate systems for which the equation is separable. These coordinate systems are explicitly known and generally do not cover the whole plane. The author constructs tensor fields which he can use to express the locus of points where the coordinates break down.

Lorentzian manifolds with special holonomy and parallel spinors

Leistner, Thomas (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

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...

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