2013/03/29 by Fatma Gökçelik, Fatma GökÇelik, GökÇelik, Fatma +8
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.DG
paper · pdf · doi:10.48550/arxiv.1303.7422
arxiv created 2013/03/29 · openalex publication_date 2013/03/29 · arxiv updated 2013/04/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we introduce an inclined curves according to parallel transport frame. Also, we define a vector field called Darboux vector field of an inclined curve in and we give a new characterization such as: "α: I ⊂ R → E4 is an inclined curve ⇔ k1 ∫ k1ds + k2 ∫ \k2 +k3ds = 0" where k1, k2, K3 are the principal curvature functions according to parallel transport frame of the curve and we give the similar characterizations such as "α: I ⊂ R → E3 is a generalized helix ⇔ k1 ∫ k1ds + k2 ∫ k2ds = 0" where k1, k2 are the principal curvature functions according to Bishop frame of the curve α. Moreover, we illustrate some examples and draw their figures with Mathematica Programme.