Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 091, 7 pages      arXiv:0708.3788      http://dx.doi.org/10.3842/SIGMA.2007.091
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces

Roman Jackiw
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received August 29, 2007, in final form September 16, 2007; Published online September 21, 2007

Abstract
Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza-Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza-Klein functions satisfy equations that coincide with the Einstein-Weyl equations in three dimensions and kink equations in two dimensions.

Key words: conformal tensors; dimensional reductions; Kaluza-Klein.

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