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Conics, Twistors, and anti-self-dual tri-Kähler metrics

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Dunajski, Maciej 
Tod, Paul 

Abstract

We describe the range of the Radon transform on the space M of irreducible conics in \CP2 in terms of natural differential operators associated to the SO(3)-structure on M=SL(3,\R)/SO(3) and its complexification. Following \cite{moraru} we show that for any function F in this range, the zero locus of F is a four-manifold admitting an anti-self-dual conformal structure which contains three different scalar-flat K"ahler metrics. The corresponding twistor space Z admits a holomorphic fibration over \CP2. In the special case where Z=\CP3∖\CP1 the twistor lines project down to a four-parameter family of conics which form triangular Poncelet pairs with a fixed base conic.

Description

Keywords

Twistor theory, anti-self-duality, tri-Kahler metrics, Radon transform

Journal Title

Asian Journal of Mathematics

Conference Name

Journal ISSN

1093-6106
1945-0036

Volume Title

Publisher

International Press of Boston, Inc.

Rights

All rights reserved
Sponsorship
The work of M.D. has been partially supported by STFC consolidated grant no. ST/P000681/1. Part of this work was done while P.T. held the Brenda Ryman Visiting Fellowship in the Sciences at Girton College, Cambridge, and he gratefully acknowledges the hospitality of the College.