In this paper, we will discuss the geometries of the Dirac-Lu space whose boundary is the third conformal space Af defined by Dirac and Lu. We firstly give the S0（3, 3） invariant pseudo- Riemannian metric with constant curvature on this space, and then discuss the timelike geodesics. Finally we get a solution of the Yang-Mills equation on it by using the reduction theorem of connections.
