Toric selfdual Einstein metrics on compact orbifolds

Research output: Contribution to journalArticle


  • D.M.J. Calderbank
  • M.A. Singer


Publication details

JournalDuke Mathematical Journal
DatePublished - 2006
Issue number2
Number of pages21
Pages (from-to)237-258
Original languageEnglish


We prove that any compact self-dual Einstein $4$-orbifold of positive scalar curvature whose isometry group contains a $2$-torus is, up to an orbifold covering, a quaternion Kähler quotient of $(k-1)$-dimensional quaternionic projective space by a $(k-2)$-torus for some $k\geq 2$. We also obtain a topological classification in terms of the intersection form of the $4$-orbifold

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