设x:M2?S3是S3中曲面,平均曲率和Gauss曲率分别为H、K,非负泛函(x)(H2 K 1)dM M W????的一个临界曲面称为一个Willmore曲面,可用4阶方程描述。一个等温曲面是指局部存在共形参数同时又是曲率参数,可用4阶方程描述。本论文证明了一个既是...设x:M2?S3是S3中曲面,平均曲率和Gauss曲率分别为H、K,非负泛函(x)(H2 K 1)dM M W????的一个临界曲面称为一个Willmore曲面,可用4阶方程描述。一个等温曲面是指局部存在共形参数同时又是曲率参数,可用4阶方程描述。本论文证明了一个既是Willmore又是等温的曲面对应椭圆方程84 1 0ww ce?????,c?0,其中?为曲面的度量的Laplacian算子,此二阶椭圆方程在Moebius群中不变。展开更多
In this paper,we study Laguerre isothermic surfaces in R3.We show that the Darboux transformation of a Laguerre isothermic surface x produces a new Laguerre isothermic surface x and their respective Laguerre Gauss map...In this paper,we study Laguerre isothermic surfaces in R3.We show that the Darboux transformation of a Laguerre isothermic surface x produces a new Laguerre isothermic surface x and their respective Laguerre Gauss maps form a Darboux pair of each other at the corresponding point.We also classify the surfaces which are both Laguerre isothermic and Laguerre minimal and show that they must be Laguerre equivalent to surfaces with vanishing mean curvature in R3,R13 or R03.展开更多
文摘设x:M2?S3是S3中曲面,平均曲率和Gauss曲率分别为H、K,非负泛函(x)(H2 K 1)dM M W????的一个临界曲面称为一个Willmore曲面,可用4阶方程描述。一个等温曲面是指局部存在共形参数同时又是曲率参数,可用4阶方程描述。本论文证明了一个既是Willmore又是等温的曲面对应椭圆方程84 1 0ww ce?????,c?0,其中?为曲面的度量的Laplacian算子,此二阶椭圆方程在Moebius群中不变。
基金supported by National Natural Science Foundation of China (Grant No.10826062)the Fundamental Research Funds for the Central Universities (Grant No.2011121040)
文摘In this paper,we study Laguerre isothermic surfaces in R3.We show that the Darboux transformation of a Laguerre isothermic surface x produces a new Laguerre isothermic surface x and their respective Laguerre Gauss maps form a Darboux pair of each other at the corresponding point.We also classify the surfaces which are both Laguerre isothermic and Laguerre minimal and show that they must be Laguerre equivalent to surfaces with vanishing mean curvature in R3,R13 or R03.
