A generalization of the momentum mapping construction for quaternionic Kähler manifolds
A generalization of the momentum mapping construction for quaternionic Kähler manifolds
复制标题
四元数凯勒流形动量映射构造的推广
DOI：
--
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
K. Galicki
中科院分区：
文献类型：
--
作者：
K. Galicki
本文给出了一种将任何具有等距的四元数Kähler流形约化为另一个等距被分割的四元数Kähler流形的方法。我们的方法是一个推广的Marsden-Weinstein建设辛流形的非辛几何的四元数凯勒的情况下。我们比较我们的结果与已知的建设Kähler和hyperKähler流形。我们还讨论了我们的结果的超对称非线性σ模型的物理和一些应用的方法的相关性。特别地，我们证明了Wolf空间可以作为四元数射影空间HP（n）的U（1）和SU（2）等价物得到.我们还构造了一个有趣的例子，紧黎曼V-流形（orbifolds）的度量是四元凯勒和不对称的。
We present a method of reduction of any quaternionic Kähler manifold with isometries to another quaternionic Kähler manifold in which the isometries are divided out. Our method is a generalization of the Marsden-Weinstein construction for symplectic manifolds to the non-symplectic geometry of the quaternionic Kähler case. We compare our results with the known construction for Kähler and hyperKähler manifolds. We also discuss the relevance of our results to the physics of supersymmetric non-linear σ-models and some applications of the method. In particular, we show that the Wolf spaces can be obtained as theU(1) andSU(2) quotients of quaternionic projective spaceHP(n). We also construct an interesting example of compact riemannianV-manifolds(orbifolds) whose metrics are quaternionic Kähler and not symmetric.