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arXiv · 2605.29083

The Cartan-K\"ahler theorem for exterior differential systems on transitive Lie algebroids

Sonja Hohloch·Tom Mestdag·Kenzo Yasaka
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Abstract

The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two versions of the Cartan-K\"ahler theorem in the case where the anchor map of the Lie algebroid is surjective. We give an illustrative example and, as a concrete application, we make use of our results in a specific case of the so-called invariant inverse problem of the calculus of variations.

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Sonja Hohloch, Tom Mestdag, Kenzo Yasaka. 2026-05-27. The Cartan-K\"ahler theorem for exterior differential systems on transitive Lie algebroids. https://arxiv.org/abs/2605.29083

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