Publication details
Holonomy groups of Lorentzian manifolds: classification, examples, and applications
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Chapter of a book |
| MU Faculty or unit | |
| Citation | |
| Description | We review recent developments in the theory of Lorentzian holonomy groups focussing on the classification results. We present the list of indecomposable, nonirreducible Lorentzian holonomy groups, explain the idea of its proof, and describe a method of constructing metrics which realise all the possible groups. This method is then used to construct many examples of metrics. Finally, we give some applications for the existence of parallel spinors and a short outlook on other signatures. As a new result we obtain the holonomy classification for indecomposable, non-irreducible Lorentzian Einstein spaces. |