Nil₃空间中的极小仿射平移曲面.

于延华; 栗倩荣; 薛 睿

Nil3 space is a Riemannian space with a Heisenberg group structure. The affine translation surfaces in Nil3 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.

RIEMANNIAN manifolds; EXPONENTIAL functions; DIFFERENTIAL equations; CURVATURE; CLASSIFICATION

Journal of Northeastern University (Natural Science), 2024, Vol 45, Issue 10, p1513

1005-3026

Academic Journal

10.12068/j.issn.1005-3026.2024.10.018