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

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

2011-04-05

arxiv.org/abs/1104.0745v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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 $n = 7$.

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