  We propose a method to modulate the bandgaps in quasi-metallic carbon
nanotubes using a transverse electric field. Unlike previous investigations, we
include curvature effects of the nanotubes by incorporating both $\pi$- and
$\sigma$-orbitals in our tight-binding calculations. The calculations show that
the small curvature-induced bandgaps decrease quadratically with electric field
amplitude to zero. As the electric field amplitude continues to increase, the
bandgap then expands in a similar manner to that presented in earlier studies.
The bandgap dependence is verified by analytical calculations, which also agree
with preceding analyses for the limit of no curvature.
