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We study harmonically trapped ultracold Bose gases with attractiveinterparticle interactions under external rotation in three spatial dimensionsand determine the critical value of the attraction strength where the gascollapses as a function of the rotation frequency. To this end we examine thestationary state in the corotating frame with a many-body approach as well aswithin the Gross-Pitaevskii theory of systems in traps with differentanisotropies. 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 findthat the collapse is not postponed in the presence of rotation. Unlikerepulsive gases, the properties of the attractive system remain practicallyunchanged under rotation in isotropic and slightly anisotropic traps.

Attractive Bose-Einstein Condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps