Killing forms on G2 and Spin7 manifolds
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0410065,
title = {Killing forms on G2 and Spin7 manifolds},
author = {Uwe Semmelmann},
journal= {arXiv preprint arXiv:math/0410065},
year = {2007}
}
Comments
15 pages