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Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action

Roger Bielawski
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Abstract

We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkaehler quotient of a flat quaternionic vector space by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n-1 whose isometry group has rank n+1 is isometric to a 3-Sasakian quotient of a sphere by a torus. As a corollary, a compact connected quaternion-Kaehler 4n-manifold with positive scalar curvature and isometry group of rank n+1 is isometric to the quaternionic projective space or the complex grassmanian.

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Roger Bielawski. 1999-01-14. Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action. https://arxiv.org/abs/math/9808134

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