  We study experimentally the line of a single vortex in a rotating prolate
Bose-Einstein condensate confined in a harmonic potential. In agreement with
predictions, we find that the vortex line is in most cases curved at the ends.
We also present measurements of the quadrupole oscillation of the condensate in
presence of a single vortex. A theoretical treatment to account for the short
time and long time behaviors of these modes is developed. Finally, we use these
measurements to infer the angular momentum per particle and relate it to the
shape of the vortex line.

Mesoscale and Nanoscale Physics