  In this work, we study helix spacelike and timelike surfaces in the
Lorentzian Berger sphere $\s_{\varepsilon}^3$, that is the three-dimensional
sphere endowed with a $1$-parameter family of Lorentzian metrics, obtained by
deforming the round metric on $\s^3$ along the fibers of the Hopf fibration
$\s^3\to \s^2({1}/{2})$ by $-\varepsilon^2$. Our main result provides a
characterization of the helix surfaces in $\s_{\varepsilon}^3$ using the
symmetries of the ambient space and a general helix in $\s_{\varepsilon}^3$,
with axis the infinitesimal generator of the Hopf fibers. Also, we construct
some explicit examples of helix surfaces in $\s_{\varepsilon}^3$.

Differential Geometry