Three-Dimensional CR Submanifolds in $S^6(1)$ with Umbilical Direction Normal to $\mathcal{D}_3$

It is well known that the sphere $S^6(1)$ admits an almost complex structure $J$ which nearly K\"{a}hler. A submanifold $M$ of Hermitian manifold called a CR if it differentiable distribution $\mathcal{D}_1$ such its orthogonal complement totally real distribution. In this case normal bundle also splits into two distributions $\mathcal{D}_3$, complex, and complement. proper three-dimensional six-dimensional $\mathcal{D}_3$ non-trivial. Here, we investigate submanifolds admitting umbilic direction to show do not exist.