We present a theoretical study of the bonding of atomic phosphorus to planar hydrocarbons and to curved graphite-like surfaces. We find that bonding of phosphorus to planar polycyclic hydrocarbons induces curvature away from the phosphorus atom, as defined by the pyramidalization angle. Similarly, bonding of atomic phosphorus to the [5,5] fulvalene-circulene semifullerene and buckminsterfullerene is only possible on the convex side of the carbon surface. On the other hand, we find the interaction of atomic phosphorus with the concave side of fullerene-like surfaces to be nonbonding for both quartet and doublet spin states. We find the prerequisite for stable epoxy-type bonds within these systems is the ability of the carbon atoms to maintain or induce curvature away from the (PC)-C-...=C bond.