  The usual concepts of topological physics, such as the Berry curvature,
cannot be applied directly to non-Hermitian systems. We show that another
object, the quantum metric, which often plays a secondary role in Hermitian
systems, becomes a crucial quantity near exceptional points in non-Hermitian
systems, where it diverges in a way that fully controls the description of
wavepacket trajectories. The quantum metric behaviour is responsible for a
constant acceleration with a fixed direction, and for a non-vanishing constant
velocity with a controllable direction. Both contributions are independent of
the wavepacket size.
