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arXiv · 1303.7422

On Inclined Curves According to Parallel Transport Frame in E4

Fatma GökÇelik·İsmail Gök·F. Nejat Ekmekci·Yusuf Yayli
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Abstract

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: "\alpha: I \subset R \rightarrow E^4 is an inclined curve \Leftrightarrow k_1 \int k_1ds + k_2 \int \k_2 +k_3ds = 0" where k_1, k_2, K_3 are the principal curvature functions according to parallel transport frame of the curve and we give the similar characterizations such as "\alpha : I \subset R \rightarrow E^3 is a generalized helix \Leftrightarrow k_1 \int k_1ds + k_2 \int k_2ds = 0" where k_1, k_2 are the principal curvature functions according to Bishop frame of the curve \alpha. Moreover, we illustrate some examples and draw their figures with Mathematica Programme.

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Fatma GökÇelik, İsmail Gök, F. Nejat Ekmekci, Yusuf Yayli. 2013-03-29. On Inclined Curves According to Parallel Transport Frame in E4. https://arxiv.org/abs/1303.7422

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