  Tomonaga-Luttinger-liquid theory is formulated for metallic carbon nanotubes
with open boundaries. Both cases of single- and multi-wall nanotubes are
discussed. Based on this theory, spatial variation of the charge density from
an edge is investigated with taking account of the shift of the chemical
potential which expresses the carrier injection to the nanotube. The charge
density has the spatially independent part and the oscillatory component. Roles
of Coulomb interaction on the amplitude of the oscillation, the wavenumbers of
it and the uniform component of the charge density are clarified.
