On totally real $3$-dimensional submanifolds of the nearly Kaehler $6$-sphere

Let $M$ be a compact $3$-dimensional totally real submanifold of the nearly Kaehler $6$-dimensional unit sphere. Let $K$ be the sectional curvature function of $M$. Then, if $K > 1/16$, $M$ is a totally geodesic submanifold (and $K \equiv 1$).