三维时空中一对复主曲率类时共形齐性曲面的分类  

Classification of time-like conformal homogeneous surfaces with a pair of complex principal curvatures in three-dimensional lorentzian space

作　　者：林燕斌 LIN Yanbin(College of Mathematics and Statistics,Minnan Normal University,Zhangzhou Fujian,363000)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2022年第3期24-29,共6页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金青年项目(2022J05167);福建省中青年教师教育科研项目(B12029);20年校长基金(L22002)。

摘　　要：研究类时共形齐性曲面x:M_(1)^(2)→R_(1)^(3),并假设其形状算子可对角化且有一对复主曲率的情形.首先通过定义共形不变度量g_(c),典则提升Y,共形切标架{E_(1),E_(2)}和典则法标架ξ,并给出了这类曲面的一个完备共形不变量系统{E_(1),E_(2)}.接下来通过可积条件,证明了这类曲面的分类定理,并构造出了对应的非杜邦曲面的例子及其共形变换子群.In this paper,we mainly study the time-like conformal surfaces x(M_(1)^(2)),where the shape operators are diagonal and have a pair of complex principal curvatures in R_(1)^(3).First,by introducing the conformal invariant metricg,the canonical lift Y,conformal tangent frame{E_(1),E_(2)} and conformal normal frameξ,we derive a complete conformal invariant system{{E_(1),E_(2)}for time-like surface in R~3.Then,we obtain classification theorem for time-like conformal homogeneous surfaces,by providing non-dupin surfaces,together with the corresponding conformal transformation subgroups.

关 键 词：复主曲率 共形不变标架 共形群 类时共形齐性曲面 

分 类 号：O186.12[理学—数学]