Einstein Spaces With Four-Parameter Holonomy Groups
- 1 May 1961
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 2 (3) , 332-336
- https://doi.org/10.1063/1.1703717
Abstract
The metric tensor is constructed for Einstein spaces which are Petrov type III and whose holonomy group is four parametric. Together with the previously known plane fronted wave solutions, this completes the study of all metrics whose holonomy groups are less than six parameter. The Killing vector equations are studied and it is found that the space cannot admit more than two independent motions.Keywords
This publication has 5 references indexed in Scilit:
- Some Applications of the Infinitesimal-Holonomy Group to the Petrov Classification of Einstein SpacesJournal of Mathematical Physics, 1961
- Classification of Four-Dimensional Riemannian SpacesJournal of Mathematical Physics, 1961
- Spherical Gravitational WavesPhysical Review Letters, 1960
- Gravitational waves in general relativity III. Exact plane wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1959
- Einstein spaces which are mapped conformally on each otherMathematische Annalen, 1925