Stable curved solitonic surfaces in nonholonomic frame

TL;DR

This paper investigates the stability and geometric properties of solitonic surfaces within nonholonomic frames, revealing nontrivial metrics influenced by hydrodynamical filaments and constrained by the Heisenberg solitonic equation.

Contribution

It introduces a new class of stable curved solitonic surfaces with nonvanishing Ricci curvature in nonholonomic frames, incorporating hydrodynamical filaments and the Heisenberg equation.

Findings

The soliton metric has non-zero Riemann curvature.

Coordinate curves are hydrodynamical filaments.

The solution extends the understanding of solitonic surface stability.

Abstract

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.