arXiv subjects

Kenzo Yasaka

Publications and source records attributed to Kenzo Yasaka.

2 recordsLinked to original sources

arXiv2026

The Cartan-Kähler theorem for exterior differential systems on transitive Lie algebroids

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.

math.DG↗

arXiv2025

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

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.

math.DG↗