关于E4中平行运输标架下的斜曲线
On Inclined Curves According to Parallel Transport Frame in E4
摘要：
本文根据平行运输标架引入了一种斜曲线。另外，我们在中定义了一个称为倾斜曲线的达布向量场的向量场，并给出了一个新的刻画，如：“α：\subset R \rightarrow E_4是倾斜曲线\Leftrightarrow k_1 \int k_1ds + k_2 \int \k_2 +k_3ds = 0”，其中k_1，k_2，K_3是曲线平行输运标架下的主曲率函数，并给出了类似的刻画，如“α：E_3是广义螺旋线\subset k_1 \int k_1ds + k_2 \int k_2ds = 0”其中k_1、k_2是曲线α的根据Bishop标架的主曲率函数。此外，我们举例说明，并绘制了他们的数字与Mathematica程序。
英文摘要：
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 \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 "α: 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 α. Moreover, we illustrate some examples and draw their figures with Mathematica Programme.
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