Differential forms, Weitzenböck formulae and foliations.

Hansklaus Rummler

Publicacions Matemàtiques (1989)

  • Volume: 33, Issue: 3, page 543-554
  • ISSN: 0214-1493

Abstract

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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.

How to cite

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Rummler, Hansklaus. "Differential forms, Weitzenböck formulae and foliations.." Publicacions Matemàtiques 33.3 (1989): 543-554. <http://eudml.org/doc/41090>.

@article{Rummler1989,
abstract = {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.},
author = {Rummler, Hansklaus},
journal = {Publicacions Matemàtiques},
keywords = {Foliaciones; Formas diferenciales; Weitzenboeck formula; differential algebra formalism; Laplacian; differential forms; foliations},
language = {eng},
number = {3},
pages = {543-554},
title = {Differential forms, Weitzenböck formulae and foliations.},
url = {http://eudml.org/doc/41090},
volume = {33},
year = {1989},
}

TY - JOUR
AU - Rummler, Hansklaus
TI - Differential forms, Weitzenböck formulae and foliations.
JO - Publicacions Matemàtiques
PY - 1989
VL - 33
IS - 3
SP - 543
EP - 554
AB - 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.
LA - eng
KW - Foliaciones; Formas diferenciales; Weitzenboeck formula; differential algebra formalism; Laplacian; differential forms; foliations
UR - http://eudml.org/doc/41090
ER -

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