Stable curved solitonic surfaces in nonholonomic frame

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.