The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916057859489792 |
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| author | Hohloch, Sonja Mestdag, Tom Yasaka, Kenzo |
| author_facet | Hohloch, Sonja Mestdag, Tom Yasaka, Kenzo |
| contents | 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-Kähler 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29083 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids Hohloch, Sonja Mestdag, Tom Yasaka, Kenzo Differential Geometry Mathematical Physics 53D17, 58A15, 58A17, 70F17 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-Kähler 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. |
| title | The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids |
| topic | Differential Geometry Mathematical Physics 53D17, 58A15, 58A17, 70F17 |
| url | https://arxiv.org/abs/2605.29083 |