  We study the generation of vortices in rotating axially elongated
magneto-optical traps, a situation which has been realized in a recent
experiment (K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Phys. Rev.
Lett. 84, 806 (2000)). We predict that at a critical frequency the condensate
experiences a symmetry breaking and changes from a convex cloud to a state with
one bended vortex. We also discuss several effects which enlarge the critical
frequency with respect to other geometries of the trap: these are, (i) the
failure of the Thomas-Fermi approximation on the transverse degrees of freedom
of the condensate, (ii) the enhancement of the transverse asymmetry of the trap
by means of rotation and (iii) the yet unobserved bending of the vortex lines.
