Weyl-Ambient Geometries

Understand

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection.

• We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds.
• We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge.
• From a top-down perspective, we show that the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry.