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01255nam a2200169Ia 4500 |
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10.3842-SIGMA.2022.027 |
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220425s2022 CNT 000 0 und d |
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|a 18150659 (ISSN)
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| 245 |
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|a Twistor Theory of Dancing Paths
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| 260 |
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|b Institute of Mathematics
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.3842/SIGMA.2022.027
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|a Given a path geometry on a surface U, we construct a causal structure on a four-manifold which is the configuration space of non-incident pairs (point, path) on U. This causal structure corresponds to a conformal structure if and only if 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 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. © 2022, Institute of Mathematics. All rights reserved.
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|a causal structures
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|a path geometry
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|a twistor theory
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| 700 |
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|a Dunajski, M.
|e author
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| 773 |
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|t Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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