Killing forms on G2 and Spin7 manifolds

Details Killing forms on G2 and Spin7 manifolds Killing forms on G2 and Spin7 manifolds

2004-10-04

arxiv.org/abs/math/0410065v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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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