### Abstract

Starting from a complex manifold S with a real-analytic c-projective 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 self-dual conformal 4-manifold 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 |
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Pages (from-to) | 4729-4760 |

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

## Profiles

### David Calderbank

- Department of Mathematical Sciences - Professor
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)

Person: Research & Teaching

## Cite this

*Transactions of the American Mathematical Society*,

*372*(7), 4729-4760. https://doi.org/10.1090/tran/7719