Abstract:

In this paper, we show that any homogeneous 3-sphere in complex Grassmanians must be a 3-dimensional ρ(SU(2))-orbit in complex Grassmanians. Then we use the representation theory of SU(2) and SU(2)×SU(2) to present a method for the construction of homogeneous 3-spheres in complex Grassmanians.

Key words: representation theory, SU(2), SU(2)×, SU(2), homogeneous 3-spheres, complex Grassmanians