Locally homogeneous pp-waves

JOURNAL OF GEOMETRY AND PHYSICS

卷:108

Article

Globke, Wolfgang¹  Leistner, Thomas¹ 

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

关键词: Lorentzian manifolds;    Killing vector fields;    Homogeneous spaces;    pp-waves;    Plane waves;    Special holonomy;   

DOI  :  10.1016/j.geomphys.2016.06.013

来源: Elsevier

【 摘 要 】

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 2-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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free