Lepage Equivalents and the Variational Bicomplex

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Saunders, David
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212110
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Lepage Equivalents and the Variational Bicomplex. David Saunders. SIGMA 20 (2024), 013, 18 pages

We show how to construct, for a Lagrangian of arbitrary order, a Lepage equivalent satisfying the closure property: that the Lepage equivalent vanishes precisely when the Lagrangian is null. The construction uses a homotopy operator for the horizontal differential of the variational bicomplex. A cho...