一类Weingarten曲面的基本方程和LAX对

The Fundamental Equations and Their Lax Pairs for a class of Weingarten Surfaces

研究三维欧氏空间中两个主曲率满足一类有理函数关系的Weingarten曲面的Gauss-Codazzi方程的分类,并给出它们的Lax对.

In this paper, we Classify the Gauss-Codazzi equations for the Weingarten surfaces in three-dimensional Euclidean space whose two principle curvatures satisfy a rational function. We also obtain their Lax pairs.