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The aim of this paper is to present the main geometrical objects on the dual1-jet bundle $J^{1*}(\cal{T},M)$ (this is the polymomentum phase space of theDe Donder-Weyl covariant Hamiltonian formulation of field theory) thatcharacterize our approach of multi-time Hamilton geometry. In this direction,we firstly introduce the geometrical concept of a nonlinear connection $N$ onthe dual 1-jet space $J^{1*}(\cal{T},M)$. Then, starting with a given$N$-linear connection $D$ on $J^{1*}(\cal{T},M)$, we describe the adaptedcomponents of the torsion, curvature and deflection distinguished tensorsattached to the $N$-linear connection $D$.

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