| Title:
|
Lorentzian manifolds with special holonomy and parallel spinors (English) |
| Author:
|
Leistner, Thomas |
| Language:
|
English |
| Journal:
|
Proceedings of the 21st Winter School "Geometry and Physics" |
| Volume:
|
|
| Issue:
|
2001 |
| Year:
|
|
| Pages:
|
[131]-159 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\bbfR^n$, and gives examples starting with K\"ahler and hyper-K\"ahler manifolds. (English) |
| MSC:
|
53C27 |
| MSC:
|
53C29 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1042.53033 |
| idMR:
|
MR1972431 |
| . |
| Date available:
|
2009-07-13T21:47:27Z |
| Last updated:
|
2012-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701694 |
| . |
