Iterated Differential Forms I: Tensors

Abstract

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.

9 pages, extended version of the published note Dokl. Math. 73, n. 2 (2006) 169

Cited by in corpus (4)

• Iterated Differential Forms III: Integral Calculus
• Iterated Differential Forms VI: Differential Equations
• Iterated Differential Forms V: C-Spectral Sequence on Infinite Jet Spaces
• Iterated Differential Forms IV: C-Spectral Sequence