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arXiv · 2307.04763

On the Total CR Twist of Transversal Curves in the 3-Sphere

Emilio Musso·Lorenzo Nicolodi
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Abstract

We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere $\mathrm S^3 \subset \mathbb C^2$. The question of the integration by quadratures of the critical curves and the problem of existence and properties of closed critical curves are addressed. A procedure for the explicit integration of general critical curves is provided and a characterization of closed curves within a specific class of general critical curves is given. Experimental evidence of the existence of infinite countably many closed critical curves is provided.

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Emilio Musso, Lorenzo Nicolodi. 2023-07-10. On the Total CR Twist of Transversal Curves in the 3-Sphere. https://doi.org/10.3842/sigma.2023.101

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