Camci, C.Kula, L.Ilarslan, K.Hacisalihoglu, H. H.2025-01-212025-01-2120131307-5624https://hdl.handle.net/20.500.12587/25208In (n+1)-dimensional Euclidean space E-n+(1), harmonic curvatures and focal curvatures of a non-degenerate curve were defined by Ozdamar and Hacisalihoglu in [7] and by Uribe-Vargas in [9], respectively. In this paper, we investigate the relations between the harmonic curvatures of a non-degenerate curve and the focal curvatures of tangent indicatrix of the curve. Also we give the relationship between the Frenet apparatus (vectors and the curvature functions) of a curve alpha in E-n (+1) and the Frenet apparatus of tangent indicatrix alpha(T) of the curve alpha. In the main theorem of the paper, we give a characterization for a curve to be a (n-1)-spherical curve in S-n by using focal curvatures of the curve. Furtermore we give that harmonic curvature of the curve is focal curvature of the tangent indicatrix.eninfo:eu-repo/semantics/closedAccessHarmonic curvature; focal curvature; spherical curve; generalized helix; tangent indicatrixArticle626369WOS:000439105700009N/A