  In this paper we study some geometrical objects (d-tensors, multi-time
semisprays of polymomenta and nonlinear connections) on the dual 1-jet vector
bundle $J^{1*}(\cal{T}, M)\to \cal{T}\times M$. Some geometrical formulas,
which connect the last two geometrical objects, are also derived. Finally, a
canonical nonlinear connection produced by a Kronecker $h$-regular multi-time
Hamiltonian is given.
