The Geometry of Singular Quaternionic Kähler Quotients
The Geometry of Singular Quaternionic Kähler Quotients
复制标题
奇异四元数凯勒商的几何
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
A. Swann
中科院分区：
文献类型：
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作者：
A. Dancer;A. Swann
通过适当的群作用，给出了四元数Kahler商的两种刻画：第一种刻画为光滑流形的并，其中一些流形具有四元数Kahler结构或局部Kahler结构；第二种刻画为四元数Kahler orbilold的并集.特别地，商总是有一个开集，它是一个光滑的四元数Kahler流形。当原流形和群是紧的时，我们在商上刻画了一个长度空间结构。给出了奇异超Kahler商和3-Sasakian商的类似刻划。
Two descriptions of quaternionic Kahler quotients by proper group actions are given: the first as a union of smooth manifolds, some of which come equipped with quaternionic Kahler or locally Kahler structures; the second as a union of quaternionic Kahler orbifolds. In particular the quotient always has an open set which is a smooth quaternionic Kahler manifold. When the original manifold and the group are compact, we describe a length space structure on the quotient. Similar descriptions of singular hyperKahler and 3-Sasakian quotients are given.