  We discuss various aspects of dimensional reduction of gravity with the
Einstein-Hilbert action supplemented by a lowest order deformation formed as
the Riemann tensor raised to powers two, three or four. In the case of R^2 we
give an explicit expression, and discuss the possibility of extended coset
symmetries, especially SL(n+1,Z) for reduction on an n-torus to three
dimensions. Then we start an investigation of the dimensional reduction of R^3
and R^4 by calculating some terms relevant for the coset formulation, aiming in
particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an
investigation of the derivative structure. We emphasise some issues concerning
the need for the introduction of non-scalar automorphic forms in order to
realise certain expected enhanced symmetries.
