  Non-Hermitian Hamiltonians are relevant to describe the features of a broad
class of physical phenomena, ranging from photonics and atomic and molecular
systems to nuclear physics and mesoscopic electronic systems. An important
question relies on the understanding of the influence of curved background on
the static and dynamical properties of non-Hermitian systems. In this work, we
study the interplay of geometry and non-Hermitian dynamics by unveiling the
existence of curvature-dependent non-Hermitian phase transitions. We
investigate a prototypical model of Dirac fermions on a sphere with an
imaginary mass term. This exactly-solvable model admits an infinite set of
curvature-dependent pseudo-Landau levels. We characterize these phases by
computing an order parameter given by the pseudo-magnetization and,
independently, the non-Hermitian fidelity susceptibility. Finally, we probe the
non-Hermitian phase transitions by computing the (generalized) Loschmidt echo
and the dynamical fidelity after a quantum quench of the imaginary mass and
find singularities in correspondence of exceptional radii of the sphere.
