In this paper, we consider the local topological structures of a class of new worldsheets, call it the rectifying worldsheets, which are generated by a class of singular worldlines. Using the classification approaches of the finite type on the tangent developables and defining the extended striction curve, this paper gives the detailed classification of the rectifying worldsheets of singular worldlines. It is demonstrated that the rectifying worldsheets of singular worldlines will appear not only in cuspidal edge and swallowtail, but cuspidal beaks under suitable conditions. Especially the singularities of rectifying worldsheets of singular worldlines are associated with curvature functions such that the singularities can be characterized by these functions. Two examples are provided to put the theoretical results into the practice of computation and classification.

中文翻译：

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识别由框架世界线生成的校正世界表的奇点

在本文中，我们考虑了一类新世界表的局部拓扑结构，称之为整流世界表，它是由一类奇异的世界线生成的。采用切可展上的有限型分类方法，定义扩展严格曲线，给出了奇异世界线的整流世界片的详细分类。证明了奇异世界线的校正世界片不仅会出现在尖角和燕尾，而且在适当的条件下会出现在尖嘴中。尤其是奇异世界线的校正世界片的奇异点与曲率函数相关联，使得奇异点可以由这些函数来表征。