On homogeneous spaces of rank one
A classification of homogeneous spaces of rank one is obtained. It is proved that they are either spherical or are induced from \(SL_2\) via a parabolic subgroup. A necessary and sufficient condition is given for a homogeneous space to have rank one. The author makes use of techniques developed by Vinberg, Popov, Luna a.o. A key step is the author's results on complexity and nilpotent orbits [Manuscr. Math. 83, No. 3-4, 223-237 (1994; Zbl 0822.14024)]. He also obtains an embedding characterization of homogeneous spaces of rank one.
scientific article; zbMATH DE number 828210