Riemann and Hamilton; help

[Blackforest]

Does someone here knows something about how tensor of curvature (Riemann) and the hamilton operator associated with a particle are connected ? Makes this question sense ? Thanks

[Blackforest]

I suppose that I should precise my question or what I exactly mean with this question. Because we know that a) the Hamiltonian operator represents the energetic state of the particle; b) the Riemann-Christoffel tensor is proportional to the stress energy tensor of a physical system, could it be that some connections exist between the Hamiltonian operator and the Riemann-...tensor ?