The electronic structure of some relevant carbon fullerenes are determined by using a sp-electron tight-binding Hamiltonian including Coulomb interactions in the Hartree-Fock approximation. Surfaces with positive, non-positive and mixed curvatures are considered in order to study the effect of the local environment on the relevant electronic properties. Nanotubes having different diameters and helicities are analyzed and the results are compared with previous calculations. In each case, the equilibrium bond-length R is optimized by maximizing the cohesive energy E-coh(N). The perspectives and extensions of this study are also discussed.