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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 manifold and , and gives examples starting with Kähler and hyper-Kähler manifolds.
Leistner, Thomas. "Lorentzian manifolds with special holonomy and parallel spinors." Proceedings of the 21st Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2002. [131]-159. <http://eudml.org/doc/221383>.
@inProceedings{Leistner2002, abstract = {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 $\mathbb \{R\}^n$, and gives examples starting with Kähler and hyper-Kähler manifolds.}, author = {Leistner, Thomas}, booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"}, keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)}, location = {Palermo}, pages = {[131]-159}, publisher = {Circolo Matematico di Palermo}, title = {Lorentzian manifolds with special holonomy and parallel spinors}, url = {http://eudml.org/doc/221383}, year = {2002}, }
TY - CLSWK AU - Leistner, Thomas TI - Lorentzian manifolds with special holonomy and parallel spinors T2 - Proceedings of the 21st Winter School "Geometry and Physics" PY - 2002 CY - Palermo PB - Circolo Matematico di Palermo SP - [131] EP - 159 AB - 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 $\mathbb {R}^n$, and gives examples starting with Kähler and hyper-Kähler manifolds. KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic) UR - http://eudml.org/doc/221383 ER -