  For a Bose-Einstein condensate placed in a rotating trap, we give a
simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi
regime, which only depends on the number and shape of the vortex lines.
  Then we check numerically that when there is one vortex line, our simplified
expression leads to solutions with a bent vortex for a range of rotationnal
velocities and trap parameters which are consistent with the experiments.
