no. G6
Mécanique
Symmetric Divergence-free tensors in the Calculus of Variations
Serre, Denis1
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, Tome 360 (2022) no. G6, 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.330
Serre, Denis 1

1 École Normale Supérieure de Lyon, U.M.P.A., UMR CNRS-ENSL # 5669. 46 allée d’Italie, 69364 Lyon cedex 07, France 
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Serre, Denis. Symmetric Divergence-free tensors in the Calculus of Variations. Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 653-663. doi : 10.5802/crmath.330. http://www.numdam.org/articles/10.5802/crmath.330/

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