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

2025/07/19 by Mestdag, Tom, Yasaka, Kenzo
#53D17 #53Z05 #58A15 #70F17 #70G65 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.14678

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.

Citations

• Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries
• Algebraic Constructions in the Category of Lie Algebroids

Related

• Intersection between the geometry of generalized Lie algebroids and some aspects of interior and exterior differential systems
• Differential calculus on a Lie algebroid and Poisson manifolds
• Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries
• Exterior differential calculus in generalized Lie algebras(algebroids) category with applications to interior and exterior algebraic(differential) systems
• Algebraic constructions in the category of vector bundles