Mathematics, Volume 10, Issue 8 (April-2 2022) – 150 articles
Lepage forms represent a far-going generalization of a 1-form, introduced by E. Cartan in the 1920s within the framework of the calculus of variations of simple integrals and classical mechanics. The generalization, offered by D. Krupka, is motivated by the work of Th. Lepage in the 1940s. These objects define the same variational functional as it is prescribed by a given Lagrangian, and moreover, variational objects (as variations, extremals, or Noether’s type invariance) are globally characterized in terms of geometric operations acting on the Lepage equivalents of a Lagrangian.
Here, a second-order extension of the fundamental Lepage form of the calculus of variations over fibered manifolds with 2-dimensional base is described via order-reducibility of the generalized Poincaré–Cartan form. View this paper
- Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
- You may sign up for e-mail alerts to receive table of contents of newly released issues.
- PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.