Where I can find more information on this? It seems really interesting. Can gravity be thought of as the curvature of the Lie group of symmetries under diffeomorphisms?The other gauge forces -- electromagnetism, weak, and strong nuclear -- can be interpreted as curvatures, but not of ordinary space. Instead, the forces correspond to curvatures in the abstract symmetry space associated with each force: U(1) for EM, SU(2) for weak, and SU(3) for the strong force. This is rather far afield from the OP; I mention it here only for completeness.