A distinguished riemannian geometrization for quadratic Hamiltonians of polymomenta

A. Oana; M. Neagu

Authors

A. Oana Transilvania University of Brasov, Romania
M. Neagu Transilvania University of Brasov, Romania

Keywords:

dual 1-jet spaces, metrical multi-time Hamilton spaces, nonlinear connections, generalized Cartan canonical N-linear connection, d-torsions and d-curvatures

Abstract

In this paper we construct a distinguished Riemannian geometrization on the dual 1-jet space J1_(T ,M) for the multi-time quadratic Hamiltonian function H = h_ab(t)g^ij(t, x)p_i^ap^b_j + U_(a)⁽ⁱ⁾(t, x)p_i^a + $F.gif$ (t, x). Our geometrization includes a nonlinear connection N, a generalized Cartan canonical N-linear connection CΓ(N) (together with its local d-torsions and d-curvatures), naturally provided by the given quadratic Hamiltonian function depending on polymomenta.