  We report a detailed study of the vibrational properties of BN single-walled
nanotubes and of the BN monolayer. Our results have been obtained from a
well-established Tight-Binding model complemented with an electrostatic model
to account for the long-range interactions arising from the polar nature of the
material, and which are not included in the Tight-Binding model. Our study
provides a wealth of data for the BN monolayer and nanotubes, such as phonon
band structure, vibrational density of states, elastic constants, etc. For the
nanotubes we obtain the behavior of the optically active modes as a function of
the structural parameters, and we compare their frequencies with those derived
from a zone-folding treatment applied to the phonon frequencies of the BN
monolayer, finding general good agreement between the two.
