Classification of compact transformation groups on complex quadrics with codimension one orbits
Classification of compact transformation groups on complex quadrics with codimension one orbits
复制标题
余维一轨道复二次曲面上紧变换群的分类
DOI：
10.18910/9615
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发表时间：
2009
影响因子：
0.4
通讯作者：
S. Kuroki
中科院分区：
文献类型：
--
作者：
S. Kuroki
设G是紧连通李群，M是可被4整除的真实的维数的有理上同调复二次曲面（其中dim M ≠ 4）.本文的目的是对（G，M）进行分类，使得G光滑地作用在M上，余维为1的主轨道。有八个这样的对本质同构。基础流形M与真正的复二次曲面除了一对之外都是同构的。
Let G be a compact connected Lie group and M a rational cohomology complex quadric of real dimension divisible by 4 (where dim M ̸= 4). The aim of this paper is to classify pairs (G,M) such that G acts smoothly on M with codimension one principal orbits. There exist eight such pairs up to essential isomorphism. The underlying manifold M is diffeomorphic to the genuine complex quadric except one pair.