### 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. (C) 1999 American Institute of Physics. [S0022-2488(99)01103-2].

Original language | English |
---|---|

Pages (from-to) | 1466-1478 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 40 |

Publication status | Published - 1999 |

### Keywords

- GENERAL-RELATIVITY
- FIXED-POINTS
- VECTOR-FIELDS
- COLLINEATIONS

### Cite this

*Journal of Mathematical Physics*,

*40*, 1466-1478.

**Classification and conformal symmetry in three-dimensional space-times.** / Hall, G S ; Capocci, M S .

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 40, pp. 1466-1478.

}

TY - JOUR

T1 - Classification and conformal symmetry in three-dimensional space-times

AU - Hall, G S

AU - Capocci, M S

PY - 1999

Y1 - 1999

N2 - 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. (C) 1999 American Institute of Physics. [S0022-2488(99)01103-2].

AB - 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. (C) 1999 American Institute of Physics. [S0022-2488(99)01103-2].

KW - GENERAL-RELATIVITY

KW - FIXED-POINTS

KW - VECTOR-FIELDS

KW - COLLINEATIONS

M3 - Article

VL - 40

SP - 1466

EP - 1478

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -