Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces

TL;DR

This paper explores how conformal tensors reduce dimensionally via Kaluza-Klein methods, revealing connections to Einstein-Weyl and kink equations in lower dimensions.

Contribution

It provides explicit formulas for reducing conformal tensors and links the vanishing of higher-dimensional tensors to Einstein-Weyl and kink equations in lower dimensions.

Findings

Explicit reduction formulas for conformal tensors from 4D to 3D and 3D to 2D.

Higher-dimensional conformal flatness implies Einstein-Weyl and kink equations in lower dimensions.

Connections between conformal geometry and lower-dimensional field equations.

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.