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

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.