The Weitzenböck Machine

Abstract

In this article we give a unified treatment of the construction of all possible Weitzenböck formulas for all irreducible, non--symmetric holonomy groups. The resulting classification is two--fold, we construct explicitly a basis of the space of Weitzenböck formulas on the one hand and characterize Weitzenböck formulas as eigenvectors for an explicitly known matrix on the other. Both classifications allow us to find tailor--suit Weitzenböck formulas for applications like eigenvalue estimates or Betti number estimates.