论文标题
E^4的曲线上的广义主教框架
Generalized Bishop frames on curves on E^4
论文作者
论文摘要
我们在常规曲线上介绍并研究了广义的主教框架，这是Frenet和Bishop框架的概括，以在更高维空间上进行常规曲线。 $ \ mathbb {e}^{4} $在常规曲线上有四种类型的广义主教框架，直到更改向量固定第一个是切线向量的向量的订单。这四种类型的框架之一是主教框架，由主教的结果，每个常规曲线都承认了这样的框架。我们表明，如果$ \ mathbb上的常规曲线$γ$ {e}^{4} $允许frenet框架，则$γ$允许所有四种类型的广义主教框架。我们还表明，如果常规曲线的切线向量的衍生物无处可消失，则曲线允许所有三种类型的广义主教框架，除了F型F框架以外，这与Frenet框架有关。
We introduce and study generalized Bishop frames on regular curves, which are generalizations of the Frenet and Bishop frames for regular curves on higher dimensional spaces. There are four types of generalized Bishop frames on regular curves on $\mathbb{E}^{4}$ up to the change of the order of vectors fixing the first one which is the tangent vector. One of these four types of frames is a Bishop frame, and by a result of Bishop, every regular curve admits such a frame. We show that if a regular curve $γ$ on $\mathbb{E}^{4}$ admits a Frenet frame, then $γ$ admits all four types of generalized Bishop frames. We also show that if the derivative of the tangent vector of a regular curve is nowhere vanishing, then the curve admits all three types of generalized Bishop frames except a frame of type F, which is related to the Frenet frame.
