  We present CO(1-0) and CO(2-1) observations of the SA(rs)bc Seyfert 2 galaxy
NGC 3147, obtained with the IRAM interferometer at 1\farcs9 $\times$1\farcs6
and 1\farcs6 $\times$1\farcs4 resolutions, respectively. A central peak seen
mainly in CO(2-1) and a ring-like structure at $r \simeq 10$\arcsec $\sim$2 kpc
dominate the CO maps. In CO(1-0) an outer spiral at $r \simeq 20$\arcsec
$\sim$4 kpc is also detected, not visible in CO(2-1) emission because it falls
outside the field-of-view of the primary beam. The kinematics of the molecular
structures are quite regular, although there is evidence for local non-circular
or streaming motions. We show that the molecular gas distribution is similar
but not exactly identical to those of star formation tracers. Using a NIR image
obtained with adaptive optics at the CFHT Telescope, we identify a weak bar in
NGC 3147, which is classified as non-barred galaxy in the optical. We then
compute the gravity torques exerted by this stellar bar on the gas. We find
that the gas inside the inner CO ring is subject to a net negative torque and
loses angular momentum. This is expected for gas at the UHR, just inside the
corotation resonance of the stellar bar. In contrast, the gas outside
corotation, in the spiral arms comprising the outer spiral structure, suffers
positive torques and is driven outwards. We conclude that some molecular gas is
presently flowing into the central region, since we find negative torques down
to the resolution limit of our images.
