  We study harmonically trapped ultracold Bose gases with attractive
interparticle interactions under external rotation in three spatial dimensions
and determine the critical value of the attraction strength where the gas
collapses as a function of the rotation frequency. To this end we examine the
stationary state in the corotating frame with a many-body approach as well as
within the Gross-Pitaevskii theory of systems in traps with different
anisotropies. In contrast to recently reported results [N. A. Jamaludin, N. G.
Parker, and A. M. Martin, Phys. Rev. A \textbf{77}, 051603(R) (2008)], we find
that the collapse is not postponed in the presence of rotation. Unlike
repulsive gases, the properties of the attractive system remain practically
unchanged under rotation in isotropic and slightly anisotropic traps.
