Dimensional reduction of Conformal Tensors

Abstract:
Analogously to the Gasuss-Codazzi reduction of the Riemann tensor, we present dimensional reductions of the conformal tensor, which in dimension greater than three is the Weyl tensor, while in three dimensions it is the Cotton tensor. The formalism is especially interesting in the four to three reduction, and in the the three to two reduction, because the Weyl tensor vanishes in three dimensions.