  Topological energy bands have important geometrical properties described by
the Berry curvature. We show that the Berry curvature changes the hydrodynamic
equations of motion for a trapped Bose-Einstein condensate, and causes
significant modifications to the collective mode frequencies. We illustrate our
results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman
field. Using an operator approach, we derive the effects of Berry curvature on
the dipole mode in very general settings. We show that the sizes of these
effects can be large and readily detected in experiment. Collective modes
therefore provide a sensitive way to measure geometrical properties of energy
bands.
