R2,1中类空曲面H=1上的Bäcklund变换

数学物理学报 ›› 2012, Vol. 32 ›› Issue (3): 500-509.

R^2,1中类空曲面H=1上的Bäcklund变换

周扣华¹|田畴²

1.扬州大学数学科学学院江苏扬州 225002；2.中国科学技术大学数学系合肥 230026

收稿日期:2009-12-13 修回日期:2011-09-25 出版日期:2012-06-25 发布日期:2012-06-25
基金资助:
国家自然科学基金(10571149)资助

Bäcklund Transformation on Space-like Surfaces with H=1 in R^2,1

ZHOU Kou-Hua¹, TIAN Chou²

1.School of Mathematics Sciences, Yangzhou University, Jiangsu Yangzhou |225002；2.Department of Mathematics,\ University of Science and Technology of China, Hefei 230026

Received:2009-12-13 Revised:2011-09-25 Online:2012-06-25 Published:2012-06-25
Supported by:
国家自然科学基金(10571149)资助

摘要/Abstract

摘要：

考虑通过线汇将三维欧氏空间R³中具有常高斯曲率(K=-1)曲面的古典Bäcklund理论推广到三维Minkowski空间R^2,1中具有常平均曲率(H=1)
的类空曲面中去, 进一步, 作者利用所得Bäcklund变换由一个已知的常平均曲率类空曲面去构造一系列新的曲面.

关键词: Bäcklund 变换, 类空曲面, 平均曲率

Abstract:

In this paper, one generalizes the classical Bäcklund theorem on the surfaces with constant Gaussian curvature(CGC) K=-1in R³ to space-like surfaces with constant mean curvature(CMC) H=1 in R^2,1 by using a line congruence. Further, one constructs a family of surfaces with constant mean curvature from a known one by Bäcklund transformation.

Key words: Bäcklund transformation, Space-like surface, Mean curvature

中图分类号:

53A10

周扣华, 田畴. R^2,1中类空曲面H=1上的Bäcklund变换[J]. 数学物理学报, 2012, 32(3): 500-509.

ZHOU Kou-Hua, TIAN Chou. Bäcklund Transformation on Space-like Surfaces with H=1 in R^2,1[J]. Acta mathematica scientia,Series A, 2012, 32(3): 500-509.

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