no. 5
Differential Geometry
Canonical semisprays for higher order Lagrange spaces
[Sémi-gerbes canoniques pour les espaces lagrangiens d'ordre supérieur]

Présenté par : Étienne Ghys

Bucataru, Ioan1
1 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, 700506, Romania
Comptes Rendus. Mathématique, Tome 345 (2007) no. 5, pp. 269-272.

Nous obtenons que la sémi-gerbe canonique d'un Lagrangien régulier d'ordre k est uniquement déterminée par deux un-formes Cartan–Poincaré associées. Autrement dit, la sémi-gerbe canonique est uniquement déterminée par sa structure présimplectique canonique et par une des une-formes Cartan–Poincaré. Nous prouvons que ce champ de vecteurs d'ordre k+1 est déterminée par un problème variationel pour lequel seulement la partie verticale de la courbe varie.

We show that the canonical semispray of a regular Lagrangian of order k is uniquely determined by two associated Cartan–Poincaré one-forms. Equivalently, the canonical semispray is uniquely determined by its canonical presymplectic structure and one of the Cartan–Poincaré one-forms. We prove that this k+1 order vector field is determined by a variational problem, for which only the vertical part of the curve is varied.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.027
Bucataru, Ioan 1

1 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, 700506, Romania 
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Bucataru, Ioan. Canonical semisprays for higher order Lagrange spaces. Comptes Rendus. Mathématique, Tome 345 (2007) no. 5, pp. 269-272. doi : 10.1016/j.crma.2007.07.027. http://www.numdam.org/articles/10.1016/j.crma.2007.07.027/

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