Abstract
Starting from a complex manifold S with a realanalytic cprojective structure whose curvature has type (1, 1), and a complex line bundle L → S with a connection whose curvature has type (1, 1), we construct the twistor space Z of a quaternionic manifold M with a quaternionic circle action which contains S as a totally complex submanifold fixed by the action. This extends a construction of hypercomplex manifolds, including hyperkähler metrics on cotangent bundles, obtained independently by Feix and Kaledin. When S is a Riemann surface, M is a selfdual conformal 4manifold and the quotient of M by the circle action is an Einstein–Weyl manifold with an asymptotically hyperbolic end, and our construction coincides with the construction presented by Borówka. The extension also applies to quaternionic Kähler manifolds with circle actions, as studied by Haydys and Hitchin.
Original language  English 

Pages (fromto)  47294760 
Number of pages  32 
Journal  Transactions of the American Mathematical Society 
Volume  372 
Issue number  7 
Early online date  4 Jan 2019 
DOIs  
Publication status  Published  1 Oct 2019 
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
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Profiles

David Calderbank
 Department of Mathematical Sciences  Professor
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching