Öztürk, Günay2024-09-122024-09-122018-03-011225-6951https://doi.org/10.5666/KMJ.2018.58.1.117https://hdl.handle.net/11452/44656The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space E-n. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space E-n. Further, we obtain some results on these type of curves in E-3 and E-4, respectively.eninfo:eu-repo/semantics/closedAccessCurvaturesVerticesFrenet curveInvolutesEvolutesScience & technologyPhysical sciencesMathematicsArticle00043522460001111713558110.5666/KMJ.2018.58.1.117