  For a Bose-Einstein condensate placed in a rotating trap, we study the
simplified energy of a vortex line derived in Aftalion-Riviere Phys. Rev. A 64,
043611 (2001) in order to determine the shape of the vortex line according to
the rotational velocity and the elongation of the condensate. The energy
reflects the competition between the length of the vortex which needs to be
minimized taking into account the anisotropy of the trap and the rotation term
which pushes the vortex along the z axis. We prove that if the condensate has
the shape of a pancake, the vortex stays straight along the z axis while in the
case of a cigar, the vortex is bent.

Mesoscale and Nanoscale Physics