On the set of complex points of a 2-sphere

Let $G$ be a strictly pseudoconvex domain in ${\mathbb{C}}^2$ with $C^{\mathrm{\infty }}$-smooth boundary $\mathrm{\partial }G$. Let $S$ be a 2-dimensional sphere embedded into $\mathrm{\partial }G$. Denote by $\mathcal{E}$ the set of all complex points on $S$. We study how the structure of the set $\mathcal{E}$ depends on the smoothness of $S$