具有局部三Hamilton作用的完备超kaehler 4 n-流形
Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action
摘要：
本文对标题中提到的具有有限拓扑型的流形进行了分类。也就是说，我们证明了任何这样的连通M同构于一个平坦的四元数向量空间的超kaehler商的阿贝尔群。证明了等距群秩为n+1的4 n-1维紧致连通和单连通3-Sasakian流形等距于球面的3-Sasakian商.作为推论，具有正数量曲率和n+1秩等距群的紧致连通四元数Kaehler 4 n-流形等距于四元数射影空间或复Grassman空间.
英文摘要：
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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