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Killing forms on G2 and Spin7 manifolds

Uwe Semmelmann
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Abstract

Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We show that on a compact manifold with holonomy G2 or Spin7 any Killing form has to be parallel. The main tool is a universal Weitzenboeck formula. We show how such a formula can be obtained for any given holonomy group and any representation defining a vector bundle.

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Uwe Semmelmann. 2004-10-04. Killing forms on G2 and Spin7 manifolds. https://arxiv.org/abs/math/0410065

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