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# Symmetric Divergence-free tensors in the calculus of variations

Abstract : Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called second'' variational principle, where the argument of the Lagrangian is a closed differential form. Divergence-free tensors are nothing but the second form of the Euler--Lagrange equations. The symmetry is associated with the invariance of the Lagrangian density upon the action of some orthogonal group.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-ens-lyon.archives-ouvertes.fr/ensl-03333651
Contributor : Denis Serre Connect in order to contact the contributor
Submitted on : Monday, September 6, 2021 - 3:49:21 PM
Last modification on : Wednesday, September 8, 2021 - 3:24:30 AM

### Files

Variations2.pdf
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### Identifiers

• HAL Id : ensl-03333651, version 2
• ARXIV : 2109.01448

### Citation

Denis Serre. Symmetric Divergence-free tensors in the calculus of variations. 2021. ⟨ensl-03333651v2⟩

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