Stable 3-spheres in ${\mathbb{C}}^3$

By only using spectral theory of the Laplace operator on spheres, we prove that the unit 3-dimensional sphere of a 2-dimensional complex subspace of ${\mathbb{C}}^3$ is a $\mathrm{\Omega }$-stable submanifold with parallel mean curvature, when $\mathrm{\Omega }$ is the K"ahler calibration of rank 4 of ${\mathbb{C}}^3$.