# Iterated differential forms: Tensors

@article{Vinogradov2006IteratedDF, title={Iterated differential forms: Tensors}, author={Alexandre M. Vinogradov and Luca Vitagliano}, journal={Doklady Mathematics}, year={2006}, volume={73}, pages={169-171} }

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

### Iterated differential forms III: Integral calculus

- 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…

### Iterated differential forms IV: The ℰ-spectral sequence

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- 2007

For the multiple differential algebra of iterated differential forms [1, 2, 3, 4] on a diffiety (

### Iterated differential forms: Λk − 1-spectral sequence on infinitely prolonged equations

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### Iterated differential forms: The Λk − 1-spectral sequence on infinite jets

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- 2007

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…

### Logic of differential calculus and the zoo of geometric strujctures

- Mathematics
- 2015

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…

### On the Van Est homomorphism for Lie groupoids

- MathematicsL’Enseignement Mathématique
- 2015

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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