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Affine Connection Complexes

Affine Connection Complexes Affine connections of 1-forms, rather than vector fields, induce complexes that project to the de Rham complexes of the underlying manifolds. This observation provides short direct proofs of Bianchi identities, existence and uniqueness of Levi-Civita connections, and symmetries of the Riemann curvature tensor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Affine Connection Complexes

Acta Applicandae Mathematicae , Volume 59 (2) – Oct 16, 2004

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1006341330965
Publisher site
See Article on Publisher Site

Abstract

Affine connections of 1-forms, rather than vector fields, induce complexes that project to the de Rham complexes of the underlying manifolds. This observation provides short direct proofs of Bianchi identities, existence and uniqueness of Levi-Civita connections, and symmetries of the Riemann curvature tensor.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 16, 2004

There are no references for this article.