Differential Geometric Aspects of the Cartan Form: Symmetry Theory
Mathematics and Natural Sciences
This paper demonstrates that the classical Cartan form θ1L is not adequate for the determination of all the natural symmetries and conservation laws for a Lagrangian L. It is shown that the various extensions θ2L,..., θrL of the classical Cartan form, introduced in recent papers, give larger symmetry groups: G1⊆G2⊆⋅⋅⋅⊆Gr. This paper also introduces the notion of contact equivalent Lagrangians, which serves to clarify the idea that different Lagrangians can give rise to the same variational and symmetry theories.
Journal of Mathematical Physics
(1987). Differential Geometric Aspects of the Cartan Form: Symmetry Theory. Journal of Mathematical Physics, 28(10).
Available at: https://aquila.usm.edu/fac_pubs/20710