  We investigated the ground state wave function and free expansion of a
trapped dipolar condensate. We find that dipolar interaction may induce both
biconcave and dumbbell density profiles in, respectively, the pancake- and
cigar-shaped traps. On the parameter plane of the interaction strengths, the
density oscillation occurs only when the interaction parameters fall into
certain isolated areas. The relation between the positions of these areas and
the trap geometry is explored. By studying the free expansion of the condensate
with density oscillation, we show that the density oscillation is detectable
from the time-of-flight image.
