Constant Angle Surfaces in Lorentzian Berger Spheres

In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere S3ε, 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 −ε^2. Our main result provides a characterization of the helix surfaces in S^3_ε using the symmetries of the ambient space and a general helix in S^3_ε, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in S^3_ε