Geometric methodology for analyzing timelike curve flows in Minkowski space (Q6542426)

It is well known that many classical completely integrable equations appear in a purely differential geometric context, e.g., the nonlinear Schrödinger equation is tightly related to the binormal motion of curves in 3-dimensional Euclidean space. In the present paper, the rigid motion of time-like curves in 3-dimensional Minkowski space is studied. By using arc length parametrization of the curves and three different moving frames, the authors find geometric interpretations of a third order vector nonlinear evolution equation that is viewed as an integrable generalization of the classical Heisenberg ferromagnetic model. Geometric relations (geometric equivalences) between that generalization and systems of modified KdV type equations are established.