By performing an analytical study of the electronic structure of metallic c
arbon nanotubes, we show that the local density of states exhibits well-def
ined oscillations as a function of the nanotube radius. The periods of such
oscillations are obtained from size quantization effects derived from fold
ing up finite graphene sheets into tubular structures. A clear analogy with
the de Haas-van Alphen effect in metals is established to explain the orig
in and features of such oscillations. Results of energy change calculations
for impurity-doped carbon nanotubes also show the same type of oscillation
s.