2012/07/12 by Fatma Gökçelik, Gökçelik, Fatma, İsmai̇l Gök +6 · 2 citations
Engineering · #14H45 #14H50 #53A04 #Differential Geometry (math.DG) #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1207.2999
openalex publication_date 2012/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The condition in terms of κand τ is so complicated but in terms of k1 and k2 is simple. So, parallel transport frame is important to make easy some complicated characterizations. Moreover, we characterize curves whose position vectors lie in their normal, rectifying and osculating planes in 4-dimensional Euclidean space E4.