Toric selfdual Einstein metrics on compact orbifolds

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 $k\ge 2$. We also obtain a topological classification in terms of the intersection form of the 4-orbifold.

14 pages; substantially revised with the addition of a new classification result and some missing details in the proofs

References in corpus (3)

• Einstein metrics and complex singularities
• M-theory compactifications on certain `toric' cones of $G_2$ holonomy
• M-theory on `toric' G_2 cones and its type II reduction

Cited by in corpus (9)

• On Conformally Kaehler, Einstein Manifolds
• The Calabi flow on Kähler surface with bounded Sobolev constant
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
• Compact anti-self-dual orbifolds with torus actions
• Continued fractions and Einstein manifolds of infinite topological type
• Scalar-flat Kähler orbifolds via quaternionic-complex reduction
• An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces
• Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces
• Self Dual Einstein Orbifolds with Few Symmetries as Quaternion Kaehler Quotients