Conformal and Curvature inheritance symmetries on Siklos space-times

Considering the Siklos spacetimes, which are among the most important known spaces in geometry and physics, we study conformal motion and curvature inheritance symmetries on these spacetimes. Initially, we classify the conformal vector fields on these spacetimes and show that there exists a large family of proper conformal vector fields on Siklos spacetimes. In particular, we specify these vector fields on an important family of Siklos spacetimes and show that proper conformal vector fields do not exist on Defris, Kaigorodov and Ozsv? th spacetimes. Then we classify the vector fields that generate the curvature inheritance symmetry on Siklos spacetimes, which only occur on conformally flat spaces. Furthermore, we show that when the function H in Siklos spacetimes is a non-constant function of x₃ (which include significant and intelligent spacetimes), there are no vector fields that generate the proper curvature inheritance symmetry.