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Classification and conformal symmetry in three-dimensional space–times
Abstract
Three-dimensional manifolds admitting Lorentz metrics are studied. The first part of the paper gives a classification of the Ricci and curvature tensors and also of the conformal (Schouten–Cotton–York) tensor. The second part of the paper investigates Killing and conformal symmetry and also the nature of the zeros of the associated vector fields. The maximum dimension of the Killing and conformal algebras is calculated. A theorem regarding the reduction of the conformal algebra to a Killing algebra of a conformally related metric is given.
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“This comes about since the Weyl tensor in 4D is equivalent to a (complex) 3 × 3 tracefree matrix, as C α β in 3D; for a similar classification of C αβ , see [30].”
From The Cotton tensor in Riemannian spacetimes (2004) · cites this paper as [30]
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Cited by
The Cotton tensor in Riemannian spacetimes
García, A. A., Hehl, F. W., Heinicke, C., & Macías, A. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/4/024 · Cited by 148
Metadata
- Authors
- Hall, G. S., & Capocci, M. S.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1999-03-01
- Volume
- 40
- Issue
- 3
- Pages
- 1466-1478
- ISSN
- 0022-2488
- 1089-7658
- Cited by
- 19
- References
- 0
- Language
- en
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- Hall, G. S., & Capocci, M. S. (1999). Classification and conformal symmetry in three-dimensional space–times. Journal of Mathematical Physics. https://doi.org/10.1063/1.532815
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