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Symmetry, Integrability and Geometry: Methods and Applications, 2025, Volume 21, 009, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2025.009 (Mi sigma2126) 		 
Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space

Emilio Mussoa, Álvaro Pámpanob

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
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DOI: https://doi.org/10.3842/SIGMA.2025.009
URL: https://www.emis.de/journals/SIGMA/2025/009/
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.
Keywords: anti-de Sitter space, geometric transformations, KdV equation, null curves.
Funding agency Grant number
PRIN 2017JZ2SW5-004
2022AP8HZ9 003
Istituto Nazionale di Alta Matematica Francesco Severi
Authors partially supported by PRIN 2017 and PRIN 2022 “Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics” (prott. 2017JZ2SW5-004 and 2022AP8HZ9 003); and by the GNSAGA of INdAM.
Received: September 24, 2024; in final form February 5, 2025; Published online February 12, 2025
Bibliographic databases:
Document Type: Article
MSC: 37K35, 53B30
Language: English
Citation: Emilio Musso, Álvaro Pámpano, “Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space”, SIGMA, 21 (2025), 009, 18 pp.
Citation in format AMSBIB
\Bibitem{MusPam25}
\by Emilio~Musso, \'Alvaro~P\'ampano
\paper Geometric Transformations on Null Curves in the Anti-de~Sitter 3-Space
\jour SIGMA
\yr 2025
\vol 21
\papernumber 009
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma2126}
\crossref{https://doi.org/10.3842/SIGMA.2025.009}
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