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arXiv · 2507.14678

Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations

Tom Mestdag·Kenzo Yasaka
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Abstract

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our developments with several examples, including an application to dynamical systems with a symmetry group and to the invariant inverse problem of the calculus of variations.

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Tom Mestdag, Kenzo Yasaka. 2025-07-19. Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations. https://doi.org/10.1007/s13324-025-01161-8

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