On Inclined Curves According to Parallel Transport Frame in E4
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.
Keywords
Cite
@article{arxiv.1303.7422,
title = {On Inclined Curves According to Parallel Transport Frame in E4},
author = {Fatma GökÇelik and İsmail Gök and F. Nejat Ekmekci and Yusuf Yayli},
journal= {arXiv preprint arXiv:1303.7422},
year = {2013}
}