Space curve evolution and soliton equation (Q674694)

The main goal of this paper is to find the explicit solution of the following Serret-Frénet equation \[ \begin{pmatrix} t\\ n\\ b\end{pmatrix}= \begin{pmatrix} 0 & k(s) & 0\\ -k(s) & 0 & \tau(s)\\ 0 & -\tau(s) & 0\end{pmatrix} \begin{pmatrix} t\\ n\\ b\end{pmatrix},\tag{1} \] where \(k(s)\) and \(\tau(s)\) are curvature and torsion of a curve in the Euclidean 3-space, respectively. The author finds new \(k(s)\) and \(\tau(s)\) and studies (1) by using the isomorphism of groups \(\text{SO}(3)\) and \(\text{SU}(2)/\{\pm1\}\). He gives a proposition, which shows that the solution of (1) and the space curve evolution in time \(t\) can be obtained. One example is given, too.