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Toric selfdual Einstein metrics on compact orbifolds

David M. J. Calderbank·Michael A. Singer
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Abstract

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler 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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David M. J. Calderbank, Michael A. Singer. 2005-02-08. Toric selfdual Einstein metrics on compact orbifolds. https://doi.org/10.1215/s0012-7094-06-13322-7

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