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arXiv · 2609.10761

Twistor theory of Loxodromes

Maciej Dunajski·Wojciech Kryński
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Abstract

The twistor correspondence provides a duality between curves in $S^4$ and ruled surfaces in $\mathbb{CP}^3$ in which the conformal properties of the former are reflected in the projective properties of the latter. We use this to characterise a $14$--dimensional family of homogeneous ruled surfaces in $\mathbb{CP}^3$ which correspond to loxodromes in $S^4$.

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Maciej Dunajski, Wojciech Kryński. 2026-09-09. Twistor theory of Loxodromes. https://arxiv.org/abs/2609.10761

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