AI 中文总结
本文针对洛伦兹-闵可夫斯基平面中奇异曲线的包络定义模糊问题，引入含奇点的光滑曲线族，提出新的包络定义并研究其性质与奇点接触情况。
AI 中文摘要
经典的包络定义对于洛伦兹-闵可夫斯基平面中的奇异曲线较为模糊。为研究此类曲线的包络，本文引入一族可能包含奇点的光滑曲线，特别地，这些曲线可同时包含非类光与类光点。随后，本文针对此类曲线提出新的包络定义，并利用类光切数据研究其性质，还考察了曲线与包络在奇点处的接触情况。
英文摘要
Classical definitions of envelopes are vague for singular curves in the Lorentz-Minkowski plane. To study envelopes of such curves, we introduce a family of smooth curves that may admit singular points. Notably, the curves considered here may contain both non-lightlike and lightlike points. We then propose a new definition of envelopes for such curves and investigate their properties using lightlike tangential data. Furthermore, we examine the contact between the curves and their envelopes at singular points.
