Toric LeBrun metrics and Joyce metrics
Nobuhiro Honda, Jeff A. Viaclovsky

TL;DR
This paper demonstrates that on the connected sum of complex projective planes, toric LeBrun metrics are conformally equivalent to Joyce metrics with a semi-free circle action, using explicit connection forms.
Contribution
It provides an explicit conformal equivalence between toric LeBrun and Joyce metrics on certain complex surfaces, with a novel connection form construction.
Findings
Toric LeBrun metrics can be identified with Joyce metrics via conformal equivalence.
Explicit connection forms for toric LeBrun metrics are constructed.
The equivalence involves a semi-free circle action.
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.
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