Yilmaz, Suha; Nizamoglu, Suur; Turgut, Melih A note on differential geometry of the curves in \(E^4\). (English) Zbl 1151.53307 Int. J. Math. Comb. 2, 104-108 (2008). Summary: In this note, we prove that every regular curve in four dimensional Euclidean space satisfies a vector differential equation of fifth order. Thereafter, in the same space, a relation among curvatures functions of inclined curves is obtained in terms of harmonic curvatures, which is related with Smarandache geometries [L. F. Mao, Int. J. Math. Comb. 1, No. 1, 45–58 (2007; Zbl 1136.51304)]. MSC: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces 53A04 Curves in Euclidean and related spaces Keywords:Euclidean space; Frenet formulas; inclined curves; harmonic curvatures; Smarandache geometries Citations:Zbl 1136.51304 PDFBibTeX XMLCite \textit{S. Yilmaz} et al., Int. J. Math. Comb. 2008, No. 2, 104--108 (2008; Zbl 1151.53307)