主曲率满足四次函数关系的Weingarten曲面的基本方程和LAX对  

Fundamental Equations and Their Lax Pairs for for Weingarten Surfaces Whose Principal Curvatures Satisfying a Quartic Function

作　　者：江祥花[1] 曹锡芳[2] JIANG Xiang-hua CAO Xi-fang(Department of Teachers＇ Training, Zhenjiang College, Danyang 212310, China School of Mathematics, Yangzhou University, Yangzhou 225002, China)

机构地区：[1]镇江高专丹阳师范学院,江苏丹阳212310 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《数学的实践与认识》2016年第21期237-243,共7页Mathematics in Practice and Theory

摘　　要：讨论三维欧氏空间中两个主曲率满足四次函数关系的Weingarten曲面的可积性,得到其Gauss-Codazzi方程的完全分类,并给出相应的Lax对.In this paper we study the integrability for a class of Weingarten surfaces in three-dimensional Euclidean space whose principal curvatures satisfy a quartic function. We classify the Gauss-Codazzi equations for this kind of Weingarten surfaces, and give their Lax pairs.

关 键 词：Gauss—Weingarten方程 Gauss—Codazzi方程 LAX对 

分 类 号：O186.11[理学—数学]