# Iterated differential forms: Tensors

@article{Vinogradov2006IteratedDF,
title={Iterated differential forms: Tensors},
author={Alexandre M. Vinogradov and Luca Vitagliano},
year={2006},
volume={73},
pages={169-171}
}
• Published 4 May 2006
• Mathematics
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed context and, in particular, enriches it with new natural operations. Applications will be considered in subsequent notes.
6 Citations
• Mathematics
• 2007
Basic elements of integral calculus over algebras of iterated differential forms �k, k < ∞, are presented. In particular, defining complexes for modules of integral forms are described and the
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For the multiple differential algebra of iterated differential forms [1, 2, 3, 4] on a diffiety (
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In the preceding note math.DG/0610917 the $\Lambda_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic
Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed that partial
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The Van Est homomorphism for a Lie groupoid $G \rightrightarrows M$, as introduced by Weinstein-Xu, is a cochain map from the complex $C^\infty(BG)$ of groupoid cochains to the Chevalley-Eilenberg

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