  The influence of rotation on the properties of red giants is studied in the
context of the asteroseismic modelling of these stars. While red giants exhibit
low surface rotational velocities, we find that the rotational history of the
star has a large impact on its properties during the red giant phase. In
particular, for stars massive enough to ignite He burning in non-degenerate
conditions, rotational mixing induces a significant increase of the stellar
luminosity and shifts the location of the core helium burning phase to a higher
luminosity in the HR diagram. This of course results in a change of the seismic
properties of red giants at the same evolutionary state. As a consequence the
inclusion of rotation significantly changes the fundamental parameters of a red
giant star as determined by performing an asteroseismic calibration. In
particular rotation decreases the derived stellar mass and increases the age.
Depending on the rotation law assumed in the convective envelope and on the
initial velocity of the star, non-negligible values of rotational splitting can
be reached, which may complicate the observation and identification of
non-radial oscillation modes for red giants exhibiting moderate surface
rotational velocities. By comparing the effects of rotation and overshooting,
we find that the main-sequence widening and the increase of the H-burning
lifetime induced by rotation (Vini=150 km/s) are well reproduced by
non-rotating models with an overshooting parameter of 0.1, while the increase
of luminosity during the post-main sequence evolution is better reproduced by
non-rotating models with overshooting parameters twice as large. This is due to
the fact that rotation not only increases the size of the convective core but
also changes the chemical composition of the radiative zone.
