闭空间曲线的规范不变几何：在边界曲线上的应用
Gauge Invariant Geometry of Closed Space Curves: Applications to Boundary Curves of Mobius-type Strips
摘要：
我们推导出规范不变表达式的扭曲$Tw$和链接数$Lk$的封闭空间曲线，这是独立的框架用来描述曲线，从而表征曲线的内在几何。因此，我们得到了曲线的C. lugreanu-White-Fuller定理的{ \it框架无关}形式$Lk =Tw + Wr$，其中$Wr$是曲线的wrist。规范不变的扭曲和扭动与两种类型的几何相位相关的曲线。作为应用，我们研究了封闭扭带边界曲线的几何性质。有趣的是，莫比乌斯带的几何形状被挑出来的一个特征最大值，出现在几何阶段，在一定的临界宽度的带。
英文摘要：
We derive gauge-invariant expressions for the twist $Tw$ and the linking number $Lk$ of a closed space curve, that are independent of the frame used to describe the curve, and hence characterize the intrinsic geometry of the curve. We are thus led to a {\it frame-independent} version of the Călugăreanu-White-Fuller theorem $Lk =Tw + Wr$ for a curve, where $Wr$ is the writhe of the curve. The gauge-invariant twist and writhe are related to two types of geometric phases associated with the curve. As an application, we study the geometry of the boundary curves of closed twisted strips. Interestingly, the Möbius strip geometry is singled out by a characteristic maximum that appears in the geometric phases, at a certain critical width of the strip.
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