Envelopes created by curve families in the Lorentz-Minkowski plane
Differential Geometry
2026-08-05 v1
Abstract
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.
Cite
@article{arxiv.2608.04506,
title = {Envelopes created by curve families in the Lorentz-Minkowski plane},
author = {Masatomo Takahashi and Yongqiao Wang},
journal= {arXiv preprint arXiv:2608.04506},
year = {2026}
}