Isometry groups of Lorentzian manifolds of finite volume and the local geometry of compact homogeneous Lorentz spaces


Diploma Thesis, 2011

131 Pages, Grade: 1,0


Abstract or Introduction

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra contains a direct summand isomorphic to the two-dimensional special linear algebra or to a twisted Heisenbergalgebra, we also describe the geometric structure of the manifolds if they are compact.

Using these results, we investigate the local geometry of compact homogeneous Lorentz spaces whose isometry groups have non-compact connected components. It turns out that they all are reductive. We investigate the isotropy representation, curvatures and holonomy. Especially, we obtain that any Ricci-flat compact homogeneous Lorentz space is flat or has compact isometry group.

Details

Title
Isometry groups of Lorentzian manifolds of finite volume and the local geometry of compact homogeneous Lorentz spaces
College
Humboldt-University of Berlin  (Institut für Mathematik)
Grade
1,0
Author
Year
2011
Pages
131
Catalog Number
V179225
ISBN (eBook)
9783656017073
ISBN (Book)
9783656017349
File size
1185 KB
Language
English
Tags
Lorentz geometry, isometry groups, twisted Heisenberg group, oscillator group, homogeneous Lorentz spaces, reductive, Ricci curvature
Quote paper
Felix Günther (Author), 2011, Isometry groups of Lorentzian manifolds of finite volume and the local geometry of compact homogeneous Lorentz spaces, Munich, GRIN Verlag, https://www.grin.com/document/179225

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