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In this paper we construct a distinguished Riemannian geometrization on thedual 1-jet space J^{1*}(T,M) for the multi-time quadratic Hamiltonianfunctions. Our geometrization includes a nonlinear connection N, a generalizedCartan canonical N-linear connection (together with its local d-torsions andd-curvatures), naturally provided by a given quadratic Hamiltonian functiondepending on polymomenta.

A distinguished Riemannian geometrization for quadratic Hamiltonians of polymomenta