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This article is cited in 1 scientific paper (total in 1 paper)
Twistor Theory of Dancing Paths
Maciej Dunajski Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Abstract:
Given a path geometry on a surface $\mathcal{U}$, we construct a causal structure on a four-manifold which is the configuration space of non-incident pairs (point, path) on $\mathcal{U}$. This causal structure corresponds to a conformal structure if and only if $\mathcal{U}$ is a real projective plane, and the paths are lines. We give the example of the causal structure given by a symmetric sextic, which corresponds on an ${\rm SL}(2,{\mathbb R})$-invariant projective structure where the paths are ellipses of area $\pi$ centred at the origin. We shall also discuss a causal structure on a seven-dimensional manifold corresponding to non-incident pairs (point, conic) on a projective plane.
Keywords:
path geometry, twistor theory, causal structures.
Received: January 14, 2022; in final form March 28, 2022; Published online March 31, 2022
Citation:
Maciej Dunajski, “Twistor Theory of Dancing Paths”, SIGMA, 18 (2022), 027, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1821 https://www.mathnet.ru/eng/sigma/v18/p27
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Abstract page: | 46 | Full-text PDF : | 9 | References: | 7 |
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