Mo 9501391 The proposed research aims to develop a general theory of geometric transformations using Lie groups and Cartan's method of moving frames. The motivation comes from the modern study of Sine-Gordon equation and KdV equation on the one hand, and the classical study of Lie on the transformation of surfaces on the other. It has been observed by a number of differential geometers that there is a somewhat mysterious connection between these two apparently disparate fields of study. If successful, the proposed research may result in a geometric theory laying a mathematical foundation for such things as solitary wave (soliton) phenomena.
