Toric LeBrun metrics and Joyce metrics

Nobuhiro Honda, Jeff Viaclovsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2923-2934
Number of pages12
JournalGeometry and Topology
Issue number5
Publication statusPublished - 2013 Oct 16
Externally publishedYes


  • Toric self-dual metrics

ASJC Scopus subject areas

  • Geometry and Topology


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