Twistor Theory of Dancing Paths

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• ISSN: 1815-0659
• Main Author: Dunajski, Maciej
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211641
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Twistor Theory of Dancing Paths. Maciej Dunajski. SIGMA 18 (2022), 027, 13 pages

Given a path geometry on a surface , we construct a causal structure on a four-manifold which is the configuration space of non-incident pairs (point, path) on . This causal structure corresponds to a conformal structure if and only if is a real projective plane, and the paths are lines. We give th...