Nonrigidity of flat ribbons

We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons, constructed along a curve in $\mathbb{R}^{3}$. In particular, we first investigate to which extent the ruled structure determines ribbon: other words, ask whether for given $\gamma$ and ruling angle (angle between line curve's tangent) there exists well-defined ribbon. It turns out that answer is positive only up an initial condition, expressed by choice normal vector at point. then set infinitely narrow fixed terms energy. By extending well-known formula bending energy rectifying developable, introduced literature Sadowsky 1930, obtain upper bound difference energies two solutions value problem. finally draw further conclusions under some additional assumptions on $\gamma$.