  Electrons and holes on semiconducting nanotubes immersed in sluggish polar
media can undergo self-localization into polaronic states. We evaluate the
binding energy $\bpol$ of adiabatic Fr\"{o}hlich-Pekar polarons confined to a
cylindrical surface and compare it to the corresponding exciton binding energy
$\bexc$. The ratio $\bpol/\bexc$ is found to be a non-monotonic function of the
cylinder radius $R$ that can reach values of about 0.35, substantially larger
than values of about 0.2 for 2$d$ or 3$d$ systems. We argue that these findings
represent a more general crossover effect that could manifest itself in other
semiconductor nanostructures in 3$d$ polar environments. As a result of the
strong polaronic effect, the activation energy of exciton dissociation into
polaron pairs is significantly reduced which may lead to enhanced charge
separation.
