2000/01/05 by Raffaele Vitolo, R. Vitolo, Vitolo, R. · 1 citation
Engineering · Mathematics · Physics and Astronomy · #58A12 #58A20 #58E30 #58G05 #Advanced Differential Geometry Research #Composite Structure Analysis and Optimization #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:58A12 #msc:58A20 #msc:58E30 #msc:58G05
paper · pdf · doi:10.48550/arxiv.math-ph/0001009
LaTeX2e with Paul Taylor's diagrams, 38 pages, no figures. Long version of a paper appeared in Math. Proc. Camb. Phil. Soc. 125 (1999), 321-333
arxiv created 2000/01/05 · openalex publication_date 2000/01/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present an intrinsic formulation for the Helmholtz condition of local variationality using a technique introduced by Kolar that we have adapted to our context. Finally, we provide the minimal order solution to the inverse problem of the calculus of variations and a solution of the problem of the variationally trivial Lagrangian.