Symmetries and geodesics in (anti-)de Sitter spacetimes with non-expanding impulsive waves

We consider a class of exact solutions which represent non-expanding impulsive waves in backgrounds with a non-zero cosmological constant. Using a convenient five-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on test particles. Timelike geodesics in the axially symmetric Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for a vanishing cosmological constant, the symmetries and geodesics reduce to those for well known impulsive pp -waves.