Global Conference on Mathematics and Applications (GCMA)

Symmetry structures of non-static cylindrically symmetric spacetimes are classified under f(R) gravity by exploring their proper curvature collineations (CCs). Utilizing direct integration and Riemann matrix rank analysis, we extract 23 distinct geometric cases based on the behavior of the f(R) function. A detailed inspection shows that three cases fail to admit proper CCs, admitting only homothetic vector fields (HVFs). Meanwhile, 14 configurations yield proper CCs that generate an infinite-dimensional vector space (IDVS). The remaining six cases collapse into flat spacetimes, where any choice of vector field constitutes a curvature collineation.