Compact hyperkähler 4n-manifolds with a local tri-Hamiltonian Rn-action. Bielawski, R.
abstract   bibtex   
We classify those manifolds mentioned in the title which have finite topological type. Namely we show that any such connected M 4n is isomorphic to a hyperkahler quotient of a flat quaternionic vector space H d by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n \textbackslashGamma 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-Kahler 4n-manifold with positive scalar curvature and isometry group of rank n + 1 is isometric to HP n or Gr 2 (C n+2 ).
@book{bielawski_compact_nodate,
	title = {Compact hyperkähler 4n-manifolds with a local tri-{Hamiltonian} {Rn}-action},
	abstract = {We classify those manifolds mentioned in the title which have  finite topological type. Namely we show that any such connected M  4n  is  isomorphic to a hyperkahler quotient of a flat quaternionic vector space H  d  by an abelian group. We also show that a compact connected and simply  connected 3-Sasakian manifold of dimension 4n {\textbackslash}Gamma 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-Kahler 4n-manifold with positive  scalar curvature and isometry group of rank n + 1 is isometric to HP  n  or  Gr 2 (C  n+2  ).},
	author = {Bielawski, Roger}
}
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