  We study the mean Uhlmann curvature in fermionic systems undergoing a
dissipative driven phase transition. We consider a paradigmatic class of
lattice fermion systems in non-equilibrium steady-state of an open system with
local reservoirs, which are characterised by a Gaussian fermionic steady state.
In the thermodynamical limit, in systems with translational invariance we show
that a singular behaviour of the Uhlmann curvature represents a sufficient
criterion for criticalities, in the sense of diverging correlation length, and
it is not otherwise sensitive to the closure of the Liouvillian dissipative
gap. In finite size systems, we show that the scaling behaviour of the mean
Uhlmann curvature maps faithfully the phase diagram, and a relation to the
dissipative gap is put forward. We argue that the mean Uhlmann phase can shade
light upon the nature of non equilibrium steady state criticality in particular
with regard to the role played by quantum vs classical fluctuations.
