Geometric structures of non-symmetric spherical manifolds by strongly visible actions

利用强可见作用研究了复半单李群的非对称球齐性空间。本文讨论了球面空间、4-对称空间和Cayley型球面簇是不可约的仿射齐性空间，复半单李代数中的球面复幂零轨道是拟仿射的。进一步，我们给出了满足每个轨道的切片的具体描述。

We study non-symmetric spherical homogeneous spaces of complex semisimple Lie groups by strongly visible actions. We treat spherical and 4-symmetric space and a certain Cayley-type spherical variety which are irreducible affine homogeneous spaces and spherical complex nilpotent orbits in a complex semisimple Lie algebra which are quasi-affine. Further, we give a concrete description of a slice which meets every orbit.