Constant Angle Surfaces in Lorentzian Berger Spheres

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