Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces
arXiv:0708.3788 · doi:10.3842/SIGMA.2007.091
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.
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
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- The Classical Solutions of the Dimensionally Reduced Gravitational Chern-Simons Theory
- More on BPS solutions of N=2, D=4 gauged supergravity
- Kaluza-Klein reduction of conformally flat spaces
- Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects