  Domains and more generally complex manifolds whose Bergman metrics have
constant holomorphic sectional curvature are characterized. Our approach is to
treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the
Fubini-Study metric of the complex projective space of infinite dimension.
Several new domains with surprising curvature properties for their Bergman
metrics are constructed. A new conjecture is also formulated at the end of the
paper.
