  Haumea is one of the most interesting and intriguing transneptunian objects
(TNOs). It is a large, bright, fast rotator, and its spectrum indicates nearly
pure water ice on the surface. It has at least two satellites and a dynamically
related family of more than ten TNOs with very similar proper orbital
parameters and similar surface properties. The Haumean family is the only one
currently known in the transneptunian belt. Various models have been proposed
but the formation of the family remains poorly understood. In this work, we
have investigated the rotational properties of the family members and
unconfirmed family candidates with short-term variability studies, and report
the most complete review to date. We present results based on five years of
observations and report the short-term variability of five family members, and
seven candidates. The mean rotational periods, from Maxwellian fits to the
frequency distributions, are 6.27+/-1.19 h for the confirmed family members,
6.44+/-1.16 h for the candidates, and 7.65+/-0.54 h for other TNOs (without
relation to the family). According to our study, there is a suggestion that
Haumea family members rotate faster than other TNOs, however, the sample of
family member is still too limited for a secure conclusion. We also highlight
the fast rotation of 2002 GH32. This object has a 0.36+/-0.02 mag amplitude
lightcurve and a rotational period of about 3.98 h. Assuming 2002 GH32 is a
triaxial object in hydrostatic equilibrium, we derive a lower limit to the
density of 2.56 g cm^-3. This density is similar to Haumea's and much more
dense than other small TNO densities.
