Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces

Understand

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.