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

Abstract

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 $\Omega$-stable submanifold with parallel mean curvature, when $\Omega$ is the K\"ahler calibration of rank 4 of $\mathbb{C}^3$.