Distinguished Torsion, Curvature and Deflection Tensors in the Multi-Time Hamilton Geometry

Abstract

The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle $J^{1\ast }(\mathcal{T},\mathcal{M})$ (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize our approach of multi-time Hamilton geometry. In this direction, we firstly introduce the geometrical concept of a nonlinear connection $N$ on the dual 1-jet space $J^{1\ast }(\mathcal{T},\mathcal{M})$. Then, starting with a given $N$-linear connection $D$ on $J^{1\ast }(\mathcal{T},\mathcal{M})$, we describe the adapted components of the torsion, curvature and deflection distinguished tensors attached to the $N$-linear connection $D$.

30 pages