A CLASS OF FOUR-DIMENSIONAL CR SUBMANIFOLDS IN SIX DIMENSIONAL NEARLY KAHLER MANIFOLDS

We investigate four-dimensional CR submanifolds in six-dimensional strict nearly Kahler manifolds. We construct a moving frame that nicely corresponds to their CR structure and use it to investigate CR submanifolds that admit a special type of doubly twisted product structure. Moreover, we single out a class of CR submanifolds containing this type of doubly twisted submanifolds. Further, in a particular case of the sphere S-6(1), we show that the two families of four-dimensional CR submanifolds, those that admit a three-dimensional geodesic distribution and those ruled by totally geodesic spheres S-3 coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.