Differential geometry of moving surfaces and its relation to solitons
The author presents a survey of the geometrical theory of motion of curves and surfaces in the three dimensional space, and its relations with nonlinear integrable systems. The working frame is the Cartan theory of moving frames together with a Cartan connection. The formalism for the motion of curves is constructed in the Serret-Frenet frames as elements of the bundle of adapted frames. The motion of surfaces is investigated in the Gauss-Weingarten frame. The main aim is to present relations between types of motions and nonlinear equations and their soliton solutions.
scientific article; zbMATH DE number 5990109