Some classes of CR submanifolds with an umbilical section of the nearly Kahler S3 x S3

Recently, the investigation of a CR submanifolds of the nearly Kahler manifold S-3 x S-3 was started. In this paper it is proved that CR submanifolds of the nearly Kahler manifold S-3 x S-3 with umbilical sections must have dimension three and then we obtain some examples of them with distinguished vector fields. Also, we classify minimal submanifolds that have a vector field E-4 as an umbilical section. The main result is classification of the three-dimensional umbilical CR submanifolds with totally geodesic and almost complex distribution D-1. (C) 2020 Elsevier B.V. All rights reserved.