  The standard Laplace operator is a generalization of the Hodge Laplace
operator on differential forms to arbitrary geometric vector bundles,
alternatively it can be seen as generalization of the Casimir operator acting
on sections of homogeneous vector bundles over symmetric spaces to general
Riemannian manifolds. Stressing the functorial aspects of the standard Laplace
operator $\Delta$ with respect to the category of geometric vector bundles we
show that the standard Laplace operator commutes not only with all
homomorphisms, but also with a large class of natural first order differential
operators between geometric vector bundles. Several examples are included to
highlight the conclusions of this article.
