A class of four dimensional CR submanifolds of the sphere S6(1)

In this paper, we investigate four dimensional CR submanifolds of the nearly Kähler sphere S6(1) that locally have a twisted product structure of special type with respect to their CR structure, and explicitly construct them by using a sphere curve. We show that four dimensional CR submanifolds with two dimensional nullity distribution belong to this class if their totally real distribution is totally geodesic and describe them.