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 Kähler calibration of rank 4 of ${\mathbb{C}}^3$.

15 pages. v3: We add a reference of a pioneer and fundamental work due to Frank Morgan, explain its relation in the introduction, correct some typos and English grammar