  The influence of a nearest-neighbor Coulomb repulsion of strength V on the
properties of the Ferromagnetic Kondo model is analyzed using computational
techniques. The Hamiltonian studied here is defined on a chain using localized
S=1/2 spins, and one orbital per site. Special emphasis is given to the
influence of the Coulomb repulsion on the regions of phase separation recently
discovered in this family of models, as well as on the double-exchange-induced
ferromagnetic ground state. When phase separation dominates at V=0, the Coulomb
interaction breaks the large domains of the two competing phases into small
``islands'' of one phase embedded into the other. This is in agreement with
several experimental results, as discussed in the text. Vestiges of the
original phase separation regime are found in the spin structure-factor as
incommensurate peaks, even at large values of V. In the ferromagnetic regime
close to density $n=0.5$, the Coulomb interaction induces tendencies to charge
ordering without altering the fully polarized character of the state. This
regime of ``charge- ordered ferromagnetism'' may be related with experimental
observations of a similar phase by C. H. Chen and S-W. Cheong (Phys. Rev. Lett.
76, 4042 (1996)). Our results reinforce the recently introduction notion (see
e.g., S. Yunoki et al., Phys. Rev. Lett. 80, 845 (1998)) that in realistic
models for manganites analyzed with unbiased many-body techniques, the ground
state properties arise from a competition between ferromagnetism and
phase-separation/charge-ordering tendencies.
