## Geometry & Topology

### Toric LeBrun metrics and Joyce metrics

#### Abstract

We show that, on the connected sum of complex projective planes, any toric LeBrun metric can be identified with a Joyce metric admitting a semi-free circle action through an explicit conformal equivalence. A crucial ingredient of the proof is an explicit connection form for toric LeBrun metrics.

#### Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2923-2934.

Dates
Accepted: 31 May 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732691

Digital Object Identifier
doi:10.2140/gt.2013.17.2923

Mathematical Reviews number (MathSciNet)
MR3190302

Zentralblatt MATH identifier
1281.53033

Subjects
Primary: 53A30: Conformal differential geometry

Keywords
toric self-dual metrics

#### Citation

Honda, Nobuhiro; Viaclovsky, Jeff. Toric LeBrun metrics and Joyce metrics. Geom. Topol. 17 (2013), no. 5, 2923--2934. doi:10.2140/gt.2013.17.2923. https://projecteuclid.org/euclid.gt/1513732691

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