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arXiv · 0903.4544

Harmonic spinors and local deformations of the metric

Bernd Ammann·Mattias Dahl·Emmanuel Humbert
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Abstract

Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

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Bernd Ammann, Mattias Dahl, Emmanuel Humbert. 2009-03-26. Harmonic spinors and local deformations of the metric. https://doi.org/10.4310/mrl.2011.v18.n5.a10

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