The projective Cartan-Klein geometry of the Helmholtz conditions
Carlos Durán Diego Otero

We show that the Helmholtz conditions characterizing differential equations arising from variational problems can be expressed in terms of invariants of curves in a suitable Grassmann manifold.

keywords: Helmholtz conditions differential invariants Lagrangian Grassmannian Schwarzian projective differential equations
The projective symplectic geometry of higher order variational problems: Minimality conditions
Carlos Durán Diego Otero
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms self-intersections of these curves.
keywords: isotropic subspaces Lagrangian Grassmannian. Calculus of variations

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