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تسجيل مستخدم جديدNearly Kaehler and nearly parallel G_2-structures on spheres
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تأليف
Thomas Friedrich
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In some other context, the question was raised how many nearly Kahler structures exist on the sphere $S^6$ 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 $lambda = 12$ of the Laplacian acting on 2-forms. A similar result concerning nearly parallel $G_2$-structures on the round sphere $S^7$ holds, too. An alternative proof by Riemannian Killing spinors is also indicated.
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