R(2,1)中曲面的伪球线汇(英文)  

Pseudospherical congruences between surfaces in R^(2,1)

作　　者：侯传燕[1] 杨祺[1] 杨晓英[1] 

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830054

出　　处：《中国科学技术大学学报》2011年第12期1065-1074,共10页JUSTC

基　　金：Supported by the National Natural Science Foundation of China(1161048);Scientific Research Foundation for Young Teachers of Xinjiang Normal University(XJNU1010)

摘　　要：线汇通过线产生于曲面间变换的经典方法中.如果保留原始一些曲面的几何性质,这些转变是特别有趣的.线汇的两个参数族作为线空间的的曲面来研究.利用活动标架来研究线汇,给出了3维闵氏空间R2,1中常Gauss曲率曲面间统一的Backlund变换和Bianchis置换定理的证明.最后,利用定理的结果构造了一些伪球曲面.Line congruences arise from the classical method of transforming one surface to another by lines.These transformations are particularly interesting if some geometric property of the original surface is preserved.Line congruences,then,are two parameter families of lines and can be studied as surfaces in the space of lines.Here the method of moving frames was used to study line congruences.Uniform Backlund transformations between constant Gauss curvature surfaces in 3-dimensional Minkowski space R2,1 were given.Also,aproof of Bianchi’s permutability theorem for pseudospherical surfaces was provided.Finally,the results of these theorems were employed to generate some pseudospherical surfaces.

关 键 词：BACKLUND变换 伪球线汇 活动标架 

分 类 号：O186.12[理学—数学]