Noether symmetries of the minimal surface Lagrangian for Gödel-type spacetimes

We investigate the Noether symmetries of the minimal surface Lagrangian for four classes of metrics in Gödel-type spacetimes. Then, calculating the Noether symmetries for all classes, namely, classes I, II, III and IV, we determine the conserved fields corresponding to each classes, allowing us to derive a comprehensive characterization of the minimal surface equations for Gödel-type spacetimes.