On Inclined Curves According to Parallel Transport Frame in E4

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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 ∫ ₂ +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.