arXiv:math/0410065 Abstract

arXiv:math/0410065 [math.DG]Abstract References Reviews Resources

Killing forms on G2 and Spin7 manifolds

Published 2004-10-04Version 1

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.

Comments: 15 pages

Categories: math.DG

Subjects: 53C55

Keywords: killing form, spin7 manifolds, universal weitzenboeck formula, main tool, vector bundle

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