Constant Angle Surfaces in Lorentzian Berger Spheres

In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere S-epsilon(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 -> S-2(1/2) by -epsilon(2). Our main result provides a characterization of the helix surfaces in S-epsilon(3) using the symmetries of the ambient space and a general helix in S-epsilon(3), with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in S-epsilon(3).