  The geometric properties of quantum states is fully encoded by the quantum
geometric tensor. The real and imaginary parts of the quantum geometric tensor
are the quantum metric and Berry curvature, which characterize the distance and
phase difference between two nearby quantum states in Hilbert space,
respectively. For conventional Hermitian quantum systems, the quantum metric
corresponds to the fidelity susceptibility and has already been used to specify
quantum phase transitions from the geometric perspective. In this work, we
extend this wisdom to the non-Hermitian systems for revealing non-Hermitian
critical points. To be concrete, by employing numerical exact diagonalization
and analytical methods, we calculate the quantum metric and corresponding order
parameters in various non-Hermitian models, which include two non-Hermitian
generalized Aubry-Andr\'{e} models and non-Hermitian cluster and mixed-field
Ising models. We demonstrate that the quantum metric of eigenstates in these
non-Hermitian models exactly identifies the localization transitions, mobility
edges, and many-body quantum phase transitions, respectively. We further show
that this strategy is robust against the finite-size effect and different
boundary conditions.
