| |||||
0747.58006
Gotay,
Mark J.
An exterior differential systems approach to the Cartan form. (English)
[CA] Symplectic geometry and mathematical physics, Proc. Colloq., Aix-en-
Provence/ Fr. 1990, Prog. Math. 99, 160-188 (1991).
Existence of Cartan forms for general variational problems (defined by an
exterior differential system) on fibered manifolds is studied. The paper
is centered around the notion of a Lepagian equivalent, an associated problem
on a different space, which generalizes the notion Cartan forms and allows
reduction to the case without constraints. For constant rank systems a canonical
Lepagian equivalent is constructed. For classical higher order variational
problems (those defined on $k$-jet bundles for sections in a fibration)
every Cartan form can be obtained as a pull back from the canonical Lepagian
equivalent. This provides a classification of all Cartan forms for classical
variational problems.
[ C.Günther
(Libby) ]
Keywords: Cartan forms; variational problems; exterior differential
system; Lepagian equivalent
Citations:
Zbl
0741.00086