  In the recently discovered Co-oxide superconductor Na_xCoO_2*yH_2O, the
edge-shared CoO6 octahedra are trigonally contracted along the c-axis in the
CoO2-plane. We study how this CoO6 distortion affects the magnetic properties
and superconductivity in this compound by analyzing the multiorbital Hubbard
model using the fluctuation-exchange approximation. It is shown that through
generating the trigonal crystal field, the distortion pushes the Co e'g bands
up and consequently gives rise to the hole-pocket Fermi surfaces, which have
been predicted in the band calculations. As the distortion increases, the hole
pockets are enlarged and the ferromagnetic fluctuation as well as the pairing
instability increases, which is in good agreement with recent NQR results.
