Twistor Theory of Dancing Paths
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211641 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 the example of the causal structure given by a symmetric sextic, which corresponds to an SL(2, ℝ)-invariant projective structure where the paths are ellipses of area π 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.
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| ISSN: | 1815-0659 |