空间曲线的副法线曲面  

Binormal Surfaces for Space Curves

作　　者：袁媛[1] 刘会立[1] 

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）》2012年第10期1517-1520,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(11071032)

摘　　要：利用活动标架及曲线的理论与性质等研究了曲线的副法线曲面,得到了一些特殊曲线的副法线曲面的特征,特别是确定了这些曲面上的一些特征曲线.根据曲面的平均曲率、高斯曲率及主曲率函数,得到了副法线曲面的极小轨迹和常高斯曲率曲线,以及曲线的挠率中心轨迹在该曲线的副法线曲面上的特殊性质.对Mannheim侣线的副法线曲面进行了研究,结果表明,沿Mannheim曲线的两个主曲率之比为-1;Mannheim曲线是Mannheim侣线的副法线曲面的极小轨迹.The binormal surfaces were studied by using moving frame, curve theory and its properties, etc. The binormal surfaces characteristics of some special curves were obtained, and, in particular, some characteristic curves on these surfaces were determined. Based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the binormal surfaces of curves and the curves with constant Gaussian curvature were obtained as well as the special properties of the center locus of torsion on the binormal surfaces of such curves. Mannheim partner curves, as the special space curves, have good geometric and algebraic properties. The binormal surfaces of Mannheim partner curves were also studied, and the results showed that the ratio of two principal curvatures on the Mannheim curves was - 1. The results also indicated that Mannheim curves were the minimal loci of the binormal surfaces of Mannheim partner curves.

关 键 词：副法线曲面 主曲率 主方向 极小轨迹 挠率中心轨迹 

分 类 号：O186.12[理学—数学]