Conformal classes of Lorentzian surfaces with Killing fields

Abstract We study the conformal classes of two‐dimensional Lorentzian tori with (nonzero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite‐dimensional fiber. It allows us to characterize the conformal classes of tori with Killing field satisfying a condition related to the existence of conjugate points given by Mehidi.