2019/05/03 by Zbyněk Urban, Zbynek Urban, Jana Volná +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Applied mathematics #Cauchy–Riemann equations #Computer science #Constructive #Differential algebraic equation #Differential equation #Geodesic #Geometric Analysis and Curvature Flows #Homogeneous #Homotopy and Cohomology in Algebraic Topology #Integrating factor #Mathematical analysis #Mathematics #Ordinary differential equation #Solving the geodesic equations #Variational integrator #Variational principle #math.DG #msc:34A26 #msc:53C22 #msc:58A15 #msc:58E30
paper · pdf · doi:10.1142/s0219887819501068
published as Int. J. Geom. Meth. Mod. Phys. 16, No. Supp02 (2019) 1950106 · arXiv admin note: text overlap with arXiv:1812.04270
openalex publication_date 2019/05/03 · arxiv created 2019/09/10 · openalex created_date 2019/09/19 · arxiv updated 2020/04/02 · openalex updated_date 2026/08/05
The exactness equation for Lepage [Formula: see text]-forms, associated with variational systems of ordinary differential equations on smooth manifolds, is analyzed with the aim to construct a concrete global variational principle. It is shown that locally variational systems defined by homogeneous functions of degree [Formula: see text] are automatically globally variational. A new constructive method of finding a global Lagrangian is described for these systems, which include for instance the geodesic equations in Riemann and Finsler geometry.