289 research outputs found
The Weitzenb\"ock Machine
In this article we give a unified treatment of the construction of all
possible Weitzenb\"ock formulas for all irreducible, non--symmetric holonomy
groups. The resulting classification is two--fold, we construct explicitly a
basis of the space of Weitzenb\"ock formulas on the one hand and characterize
Weitzenb\"ock formulas as eigenvectors for an explicitly known matrix on the
other. Both classifications allow us to find tailor--suit Weitzenb\"ock
formulas for applications like eigenvalue estimates or Betti number estimates.Comment: 48 page
Twistor Forms on Riemannian Products
We study twistor forms on products of compact Riemannian manifolds and show
that they are defined by Killing forms on the factors. The main result of this
note is a necessary step in the classification of compact Riemannian manifolds
with non-generic holonomy carrying twistor forms.Comment: 5 page
Conformal Killing forms on Riemannian manifolds
Conformal Killing forms are a natural generalization of conformal vector
fields on Riemannian manifolds. They are defined as sections in the kernel of a
conformally invariant first order differential operator. We show the existence
of conformal Killing forms on nearly Kaehler and weak G_2-manifolds. Moreover,
we give a complete description of special conformal Killing forms. A further
result is a sharp upper bound on the dimension of the space of conformal
Killing forms.Comment: 24 page
Killing Forms on Symmetric Spaces
Killing forms on Riemannian manifolds are differential forms whose covariant
derivative is totally skew--symmetric. We show that a compact simply connected
symmetric space carries a non--parallel Killing --form () if and only
if it isometric to a Riemannian product , where is a round
sphere and
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