2026/08/05 by Masatomo Takahashi, Yongqiao Wang
Mathematics · #math.DG #msc:53B30 #msc:53C50
arxiv created 2026/08/05 · arxiv updated 2026/08/06
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.