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Roger Bielawski - Tn-invariant hyperkähler 4n-manifolds
ROGER BIELAWSKI, Max Planck Institute, Bonn, Germany | |
Tn-invariant hyperkähler 4n-manifolds |
We prove that a connected simply connected complete hyperkähler 4n-manifold of finite topological type equipped with an effective tri-Hamiltonian action of Tn is isometric to a hyperkähler quotient of a flat by . As a consequence, such manifolds are classified, up to canonical deformations by arrangements of codimension 3 affine subspaces in .
We show a similar result for two other classes of Einstein manifolds: compact 3-Sasakian and compact quaternion-Kähler with positive scalar curvature. In the latter case, we are able to conclude that such a 4n-manifold admitting a group of isometries of rank n+1 is either or .
eo@camel.math.ca