  Assuming the stability of soliton surfaces of vanishing Ricci sectional
curvature of soliton metric in the nonholonomic frame, we find a solution for
the metric in the approximation of weak constant torsion curves with constant
Frenet curvature. The computation of the Riemann tensor of the soliton metric
shows that it does not vanish and therefore the solution is nontrivial.
Heisenberg solitonic equation is also used to constrain the the soliton Riemann
metric. The new feature here is that the coordinate curves on the soliton-like
surface are composed of hydrodynamical filaments.
