Lorentzian manifolds with special holonomy and parallel spinors

Leistner, Thomas

  • Proceedings of the 21st Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page [131]-159

Abstract

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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 ℝ n , and gives examples starting with Kähler and hyper-Kähler manifolds.

How to cite

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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 -

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