The second Dirac eigenvalue of a nearly parallel G2G_2-manifold

preprint2011arXivOpen access

Abstract

We investigate the second Dirac eigenvalue on Riemannian manifolds admitting a Killing spinor. In small dimensions the whole Dirac spectrum depends on special eigenvalues on functions and 1-forms. We compute and discuss the formulas in dimension n=7n = 7.

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