Ucar, AysenurKarakuş, Fatma2025-03-232025-03-2320221694-7398https://doi.org/10.51354/mjen.937100https://search.trdizin.gov.tr/tr/yayin/detay/1138771https://hdl.handle.net/11486/3226In this paper, generalized Fermi derivative, generalized Fermi parallelism, and generalized non-rotating frame concepts are given along any curve on any hypersurface in Eⁿ⁺¹ Euclidean space. The generalized Fermi derivative of a vector field and being generalized non-rotating conditions are analyzed along the curve on the surface in Euclidean 3-space. Then a correlation is found between generalized Fermi derivative, Fermi derivative, and Levi-Civita derivative in E³. Then we examine generalized Fermi parallel vector fields and conditions of being generalized non-rotating frame with the tensor field in E⁴. Generalizations have been made in Eⁿ.eninfo:eu-repo/semantics/openAccessMikroskopiMatematikArticle10111011510.51354/mjen.9371001138771