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arXiv · 2311.11137

Integrable Flows on Null Curves in the Anti-de Sitter 3-Space

Emilio Musso·Alvaro Pampano
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Abstract

We formulate integrable flows related to the KdV hierarchy on null curves in the anti-de Sitter 3-space (${\rm AdS}$). Exploiting the specific properties of the geometry of ${\rm AdS}$, we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solutions of the lower order flow can be explicitly found in terms of periodic solutions of a Lam\'e equation. In addition, we study the evolution of non-stationary curves arising from a 3-parameter family of periodic solutions of the KdV equation.

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Emilio Musso, Alvaro Pampano. 2023-11-18. Integrable Flows on Null Curves in the Anti-de Sitter 3-Space. https://arxiv.org/abs/2311.11137

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