  Let $\mathfrak{H}$ be the Heisenberg group. From the standard CR structure
$\mathcal{H}$ of $\mathfrak{H}$ we construct the complex hyperbolic structure
of the Siegel domain. Additionally, using the same minimal data for
$\mathfrak{H}$, that is, its Sasakian structure, we provide the Siegel domain
with yet another K\"ahler structure: this structure is of unbounded negative
sectional curvature, and its complex structure does not commute with the
standard complex structure. However, we show that those two K\"ahler structures
are {\rm PCR} K\"ahler equivalent, that is to say, essentially the same when
restricted to $\mathcal{H}$.
