Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 009, 18 pages      arXiv:2312.10765      https://doi.org/10.3842/SIGMA.2025.009

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

Emilio Musso ^a and Álvaro Pámpano ^b
a) Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
^b) Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409, USA

Received September 24, 2024, in final form February 05, 2025; Published online February 12, 2025

Abstract
We provide a geometric transformation on null curves in the anti-de Sitter 3-space (AdS) which induces the Bäcklund 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.

Key words: anti-de Sitter space; geometric transformations; KdV equation; null curves.

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