  We have studied the Hubbard model with bond-charge interaction on a
triangular lattice for a half-filled band. At the point of particle-hole
symmetry the model could be analyzed in detail in two opposite regimes of the
parameter space. Using a real space renormalization group we calculate the
ground state energy and the local moment over the whole parameter space. The RG
results obey the exact results in the respective limits. In the intermediate
region of the parameter space the RG results clearly show the effects of the
non-bipartite geometry of the lattice as well as the absence of symmetry in the
reversal of the sign of the hopping matrix element.
