Nil_(3)空间中的极小仿射平移曲面  

Minimal Affine Translation Surfaces in Nil_(3)Space

作　　者：于延华[1] 栗倩荣 薛睿 YU Yan-hua;LI Qian-rong;XUE Rui(School of Sciences,Northeastern University,Shenyang 110819,China.)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2024年第10期1513-1520,共8页Journal of Northeastern University(Natural Science)

基　　金：中央高校基本科研业务费专项资金资助项目(N2104007).

摘　　要：Nil_(3)空间是带有Heisenberg群结构的黎曼空间.利用Heisenberg群的群算子构造Nil_(3)空间中的仿射平移曲面.仿射平移曲面是由两条平面曲线作为基线通过群运算生成的.由于群运算不具有交换性,选定一组基线可以生成两类不同的仿射平移曲面.之后对这两种仿射平移曲面进行分类.利用常数变易法和欧拉待定指数函数法解曲面的平均曲率等于零时所对应的微分方程,并给出不同运算下极小仿射平移曲面的分类定理.最后给出一些具体的极小仿射平移曲面,并用Mathematica画出相应的图像.Nil_(3)space is a Riemannian space with a Heisenberg group structure.The affine translation surfaces in Nil_(3)space are constructed by using the group operator of the Heisenberg group.These surfaces are generated by two planar curves as base lines through group operation.However,since group operations are not commutative,selecting the same base lines generates two types of different affine translation surfaces.Then,the two affine translation surfaces are classified.Employ the method of variation of constants and Euler’s method of indeterminate exponential functions to solve the differential equation arising when the mean curvature of a surface equal zero,and present the classification theorem for minimal affine translation surfaces under various operations.Finally,some specific minimal affine translation surfaces are given,and corresponding images are drawn using Mathematica.

关 键 词：Nil_(3)空间 仿射平移曲面 极小曲面 HEISENBERG群 平均曲率 

分 类 号：O186[理学—数学]