  A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric
quantum mechanics and they are further unified into one entity, i.e., an
extended quantum geometric tensor (QGT). The imaginary part of the extended QGT
gives a Berry curvature whereas the real part induces a metric tensor on
system's parameter manifold. This results in a unified conceptual framework to
understand and explore physical properties of $\mathcal{PT}$-symmetric systems
from a geometric perspective. To illustrate the usefulness of the extended QGT,
we show how its real part, i.e., the metric tensor, can be exploited as a tool
to detect quantum phase transitions as well as spontaneous
$\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.
