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arXiv · 2608.04506

Envelopes created by curve families in the Lorentz-Minkowski plane

Masatomo Takahashi·Yongqiao Wang
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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.

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Masatomo Takahashi, Yongqiao Wang. 2026-08-05. Envelopes created by curve families in the Lorentz-Minkowski plane. https://arxiv.org/abs/2608.04506

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