  We carried out an unbiased survey for massive dense cores in the giant
molecular cloud associated with eta Carinae with the NANTEN telescope in 12CO,
13CO, and C18O 1-0 emission lines. We identified 15 C18O cores. Two of the 15
cores are associated with IRAS point sources whose luminosities are larger than
10^4 Lo, which indicates that massive star formation is occuring within these
cores. Five cores including the two with IRAS sources are associated with MSX
point sources. We detected H13CO+ (1-0) emission toward 4 C18O cores, one of
which is associated with neither IRAS nor MSX point sources. This core shows
the presence of a bipolar molecular outflow in 12CO (2-1), which indicates that
star formation is also occuring in the core. In total, six C18O cores out of 15
are experienced star formation, and at least 2 of 15 are massive-star forming
cores in the eta Car GMC. We found that massive star formation occurs
preferentially in cores with larger column density, mass, number density, and
smaller ratio of virial mass to LTE mass Mvir/M. We also found that the cores
in the eta Car GMC are characterized by large line width and Mvir/M on average
compared to the cores in other GMCs. We investigated the origin of a large
amount of turbulence in the eta Car GMC. We propose the possibility that the
large turbulence was pre-existing when the GMC was formed, and is now
dissipating. Mechanisms such as multiple supernova explosions in the Carina
flare supershell may have contributed to form a GMC with a large amount of
turbulence.
