  By using a projective connection over the space of two-dimensional affine
connections, we are able to show that the metric interaction of Polyakov 2D
gravity with a coadjoint element arises naturally through the projective Ricci
tensor. Through the curvature invariants of Thomas-Whitehead, we are able to
define an action that could describe dynamics to the projective connection. We
discuss implications of the projective connection in higher dimensions as
related to gravitation.
