Canonical Nonlinear Connections on Jet Bundles of First Order

Abstract

The aim of this paper is to open the problem of construction of a nonlinear connection $\Gamma =(M_{(\alpha )\beta }^{(i)},N_{(\alpha )j}^{(i)})$ on the jet bundle of first order $J^1(T,M)$, which to be canonically produced by a Kronecker product vertical metrical d-tensor $G_{(i)(j)}^{(\alpha )(\beta )}=h^{\alpha \beta }{g}_{ij}$, possibly provided by multi-time dependent quadratic Lagrangians coming from various branches of theoretical physics: bosonic strings theory, electrodynamics or elasticity.

7 pages, Versions of this paper were presented at: -Workshop on Differential Geometry, Global Analysis and Lie Algebras, Aristotle University of Thessaloniki, Greece, Aug. 28-Sept. 2, 2000; -Seminar "Gh. Vranceanu", University of Bucharest, Romania, November, 2000

References in corpus (5)

• Solutions of DEs and PDEs as Potential Maps Using First Order Lagrangians
• The Geometry of Relativistic Rheonomic Lagrange Spaces
• The Geometry of Metrical Multi-time Lagrange Spaces
• The Generalized Metrical Multi-Time Lagrange Space of Relativistic Geometrical Optics
• Generalized Metrical Multi-Time Lagrange Model for General Relativity and Electromagnetism