Dil, Emre2025-03-232025-03-2320160374-48841976-8524https://doi.org/10.3938/jkps.69.1733https://hdl.handle.net/11486/4627In this paper, we study the generalized parallel transport of vectors and generalized coordinate transformations between generalized reference frames described in f(R) gravity. After constructing the generalized parallel transport relations and the generalized transformation laws in f(R) gravity, we discuss the implications of these laws and present the differences between f(R) gravity and Einstein's general relativity. For a constant Ricci scalar case with de Sitter-like behavior for a de Sitter space-time, we find that the parallel transport is invariant under the conformal transformation from general relativity to f(R) gravity. However, for a non-de Sitter space-time, parallel transport differs by an extra field term.eninfo:eu-repo/semantics/closedAccessCoordinate transformationsGeneral relativityf(R) gravityArticle69121733173810.3938/jkps.69.17332-s2.0-85007571949Q3WOS:000392143900001Q3