Form Geometry and the 'tHooft-Plebanski Action

Abstract

Riemannian geometry in four dimensions, including Einstein's equations, can be described by means of a connection that annihilates a triad of two-forms (rather than a tetrad of vector fields). Our treatment of the conformal factor of the metric differs from the original presentation of this result, due to 'tHooft. In the action the conformal factor now appears as a field to be varied.