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Co--calibrated $G_2$ structure from cuspidal cubics | | Boris Doubrov
; Maciej Dunajski
; | | Date: |
14 Jul 2011 | | Abstract: | We establish a twistor correspondence between a cuspidal cubic curve in a
complex projective plane, and a co-calibrated homogeneous $G_2$ structure on
the seven--dimensional parameter space of such cubics. Imposing the Riemannian
reality conditions leads to an explicit co--calibrated $G_2$ structure on
$SU(2, 1)/U(1)$. Cuspidal cubics and their higher degree analogues with
constant projective curvature are characterised as integral curves of 7th order
ODEs. Projective orbits of such curves are shown to be analytic continuations
of Aloff--Wallach manifolds, and it is shown that only cubics lift to a
complete family of contact rational curves in a projectivised cotangent bundle
to a projective plane. | | Source: | arXiv, 1107.2813 | | Services: | Forum | Review | PDF | Favorites | |
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