A band structure model for carbon nanotubes taking into account the de
formation potential characterizing the conformal mapping of graphene t
o tubules is presented and overlap is introduced in the pi band calcul
ations. This model corresponds to the study of a one-dimensional (1D)
system and is not simply the limit of a 2D system becoming quasi-1D. W
hile development is explicitly made for the zigzag tubules, the method
itself can also be applied to the armchair and chiral configurations
by modifying the structure factor and boundary conditions. (C) 1997 El
sevier Science S.A.