2015/03/05 by María Barbero-Liñán, Barbero-Liñán, María, Marta Farré Puiggalí +4 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #37J99 #49N45 #53C15 #53D12 #70H03 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #math-ph #math.DG #math.MP #msc:37J99 #msc:49N45 #msc:53C15 #msc:53D12 #msc:70H03
paper · pdf · doi:10.48550/arxiv.1503.01794
Comments welcome!
arxiv created 2015/03/05 · openalex publication_date 2015/03/05 · arxiv updated 2015/03/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
The language of Lagrangian submanifolds is used to extend a geometric characterization of the inverse problem of the calculus of variations on tangent bundles to regular Lie algebroids. Since not all closed sections are locally exact on Lie algebroids, the Helmholtz conditions on Lie algebroids are necessary but not sufficient, so they give a weaker definition of the inverse problem. As an application the Helmholtz conditions on Atiyah algebroids are obtained so that the relationship between the inverse problem and the reduced inverse problem by symmetries can be described. Some examples and comparison with previous approaches in the literature are provided.