Comptes Rendus
Mécanique
Symmetric Divergence-free tensors in the Calculus of Variations
Denis Serre1
1 École Normale Supérieure de Lyon, U.M.P.A., UMR CNRS-ENSL # 5669. 46 allée d’Italie, 69364 Lyon cedex 07, France
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 653-663.

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.

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DOI : 10.5802/crmath.330
Denis Serre 1

1 École Normale Supérieure de Lyon, U.M.P.A., UMR CNRS-ENSL # 5669. 46 allée d’Italie, 69364 Lyon cedex 07, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Denis Serre. Symmetric Divergence-free tensors in the Calculus of Variations. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 653-663. doi : 10.5802/crmath.330. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.330/

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