A simple closed curve α in the boundary of a genus two handlebody H is primitive if adding a 2-handle to H along α yields a solid torus. If adding a 2-handle to H along α yields a Seifert-fibered space and not a solid torus, the curve is called Seifert. If α is disjoint from an essential separating disk in H, does not bound a disk in H, and is not primitive in H, then it is said to be proper power.

As one of the background papers of the classification project of hyperbolic primitive/Seifert knots in $S^3$ whose complete list is given by Berge and the author [4], this paper classifies primitive, proper power, and Seifert curves in terms of R-R diagrams. In other words, we provide up to equivalence all possible R-R diagrams of such curves. Furthermore, we further classify all possible R-R diagrams of proper power curves with respect to an arbitrary complete set of cutting disks of a genus two handlebody.

一个简单的闭合曲线α中的一个属2柄体的边界ħ是原始若加入2-句柄ħ沿着α产生一个固体圆环。如果沿α向H添加2手柄会产生Seifert纤维状空间而不是实心圆环，则该曲线称为Seifert。如果α是从在一个基本分离盘不相交ħ，不结合在一个磁盘ħ，并且不是在原始ħ，那么它被说成是合适的功率。

作为双曲本原/ Seifert结分类项目的背景论文之一。 ${\mathrm{小号}}^3$其完整清单由Berge和作者[4]给出，本文根据RR图对原始曲线，适当的功率曲线和Seifert曲线进行了分类。换句话说，我们提供了等效的所有此类曲线的RR图。此外，我们针对属两个手柄体的任意完整切割盘，进一步分类了适当功率曲线的所有可能的RR图。