The Weitzenböck formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor. In the first part, we shall describe a certain "differential algebra formalism" which seems to be a more natural frame for those formulae than the usual calculations in local coordinates.
In this formalism there appear some interesting differential operators which may also be used to characterize local geometric properties of foliations. That is the topic of the second part.
@article{urn:eudml:doc:41090,
title = {Differential forms, Weitzenb\"ock formulae and foliations.},
journal = {Publicacions Matem\`atiques},
volume = {33},
year = {1989},
pages = {543-554},
zbl = {0701.53033},
mrnumber = {MR1038489},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41090}
}
Rummler, Hansklaus. Differential forms, Weitzenböck formulae and foliations.. Publicacions Matemàtiques, Tome 33 (1989) pp. 543-554. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41090/