Locally homogeneous pp-waves
Differential Geometry
2016-09-12 v2 Mathematical Physics
math.MP
Abstract
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on -forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classical result by Jordan, Ehlers and Kundt in dimension 4. Several examples show that our assumptions on indecomposability and the rank of the curvature are essential.
Keywords
Cite
@article{arxiv.1410.3572,
title = {Locally homogeneous pp-waves},
author = {Wolfgang Globke and Thomas Leistner},
journal= {arXiv preprint arXiv:1410.3572},
year = {2016}
}
Comments
In v2 Example 4.3 is added which shows that in the main theorems the assumption on the rank of the curvature is essential