Polar coordinates induced by actions of compact Lie groups
Polar coordinates induced by actions of compact Lie groups
复制标题
由紧李群作用引起的极坐标
DOI：
10.1090/s0002-9947-1985-0773051-1
复制
发表时间：
1985
影响因子：
1.3
通讯作者：
Jiri Dadok
中科院分区：
文献类型：
--
作者：
Jiri Dadok
设G是真实的正交群0（n）的连通李群.对于G在R '上的作用，我们构造了与所有轨道相交的线性子空间a。我们确定G存在这样一个满足所有的G-轨道正交，nally;集团的作用传递领域是明显的例子。除了少数例外，所有可能的G都是黎曼对称空间的各向同性子群。导论.设G是作用在真实的向量空间V上的紧李群，K，.）是V上的G-不变内积。有一个线性横截面a c V，
Let G be a connected Lie subgroup of the real orthogonal group 0(n). For the action of G on R', we construct linear subspaces a that intersect all orbits. We determine for which G there exists such an a meeting all the G-orbits orthogo- nally; groups that act transitively on spheres are obvious examples. With few exceptions all possible G arise as the isotropy subgroups of Riemannian symmetric spaces. Introduction. Let G be a compact Lie group acting on a real vectorspace V, and let K ,.) be a G-invariant inner product on V. Having a linear cross-section a c V of