  Phonon softening phenomena of the $\Gamma$ point optical modes including the
longitudinal optical mode, transverse optical mode and radial breathing mode in
"metallic" single wall carbon nanotubes are reviewed from a theoretical point
of view. The effect of the curvature-induced mini-energy gap on the phonon
softening which depends on the Fermi energy and chirality of the nanotube is
the main subject of this article. We adopt an effective-mass model with a
deformation-induced gauge field which provides us with a unified way to discuss
the curvature effect and the electron-phonon interaction.
