Nonstandard connections in k-cosympletic field theory

Abstract

In the jet-bundle description of time-dependent mechanics there are some elements, such as the Lagrangian energy and the construction of the Hamiltonian formalism, which require the prior choice of a connection. This situation is analyzed by Echeverría-Enríquez et al. [J. Phys. A 28, 5553–5567 (1995)]. The aim of this paper is to extend the results in that paper to first order field theory, using the k-cosymplectic formalism described by de León and co-workers [J. Math. Phys. 39, 876–893 (1998); 42, 2092–2104 (2001)]. If the trivial configuration bundle of a Lagrangian system is endowed with one connection, different from the trivial one given by the product structure, we study the consequences on the geometric elements of the theory, the dynamical equations and the variational principles.