A note on proper curvature collineations of vacuum classes of plane fronted gravitational waves in f(R) theory of gravity

Proper curvature collineations (CCs) of plane-fronted gravitational waves (GWs) in [Formula: see text] gravity are addressed in this paper. We first think about vacuum classes of plane GWs and analyze their CCs using mathematical and integration methods, and we also use a [Formula: see text] Riemann curvature matrix. This sorting results in ten cases: three where the spacetimes turn conformally flat and generate infinite-dimensional vector spaces (IDVs), and seven where CCs form IDVs.