Dimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces

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.