2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76276In some other context, the question was raised how many nearly Kähler structures exist on the sphere $§^6$ equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue $λ= 12$ of the Laplacian acting on 2-forms. A similar result concerning nearly parallel $\G_2$-structures on the round sphere $§^7$ holds, too. An alternative proof by Riemannian Killing spinors is also indicated.2 pages, Latex2eDifferential Geometry53C25; 81T30text