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arXiv · 2312.10765

Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space

Emilio Musso·Álvaro Pámpano
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Abstract

We provide a geometric transformation on null curves in the anti-de Sitter 3-space (AdS) which induces the B\"acklund transformation for the KdV equation. In addition, we show that this geometric transformation satisfies a suitable permutability theorem. We also illustrate how to implement it when the original null curve has constant bending.

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Emilio Musso, Álvaro Pámpano. 2023-12-17. Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space. https://doi.org/10.3842/sigma.2025.009

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