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The second Dirac eigenvalue of a nearly parallel $G_2$-manifold

By Thomas Friedrich

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 $n = 7$.Comment: 10 page

Topics: Mathematics - Differential Geometry, 53C25, 81T30
Year: 2011
OAI identifier: oai:arXiv.org:1104.0745
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