CONFORMAL AND CURVATURE INHERITANCE SYMMETRIES ON SIKLOS SPACE-TIMES

Abstract

Considering the Siklos spacetimes, which are among the most important known spaces in
geometry and physics, we study conformal motion and curvature inheritance symmetries 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 Ozsváth 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 the vector fields that generate the
proper curvature inheritance symmetry.