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arXiv · 2312.03363

Darboux transformations of spacelike curves in the Lorentz-Minkowski plane

Masaya Hara
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Abstract

This paper concerns (Lorentz-)Darboux transformations in the Lorentz-Minkowski plane $\mathbb{R}^{1,1}$. We use the Penrose diagram for conformal compactification and show some unique properties of Darboux transformations of spacelike curves in $\mathbb{R}^{1,1}$, especially with regard to singularities and blowup. Finally, we make some comments on Darboux transformation of type-changing curves.

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Masaya Hara. 2023-12-06. Darboux transformations of spacelike curves in the Lorentz-Minkowski plane. https://arxiv.org/abs/2312.03363

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