  Without a hybridization between the localized f- and the conduction (c-)
electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in
the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here
I show that at least for sufficiently small c-f-interaction this exact
inhomogeneous ground state is also obtained in Hartree-Fock approximation. With
hybridization the model is no longer exactly solvable, but the approximation
yields that the inhomogeneous charge-density wave (CDW) ground state remains
stable also for finite hybridization V smaller than a critical hybridization
V_c, above which no inhomogeneous CDW solution but only a homogeneous solution
is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground
state with a spontaneous polarization, i.e. there is no nonvanishing
$<c^{\dagger}f>$-expectation value in the limit of vanishing hybridization.
