| 管状曲面在曲线论中的应用 |
| |
| 引用本文： | 苏农,刘玲.管状曲面在曲线论中的应用[J].纯粹数学与应用数学,2012(1):67-72. |
| |
| 作者姓名： | 苏农 刘玲 |
| |
| 作者单位： | 北京信息科技大学数学系 |
| |
| 基金项目： | 北京市教委科研计划面上项目(SQKM201211232017);北京信息科技大学科研基金(5026010949) |
| |
| 摘 要： | 研究了围绕曲线的管状曲面上的曲率线，渐近线与测地线，给出它们的方程，揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系，采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．
|
| 关 键 词： | 管状曲面 渐近线 测地线 Bertrand曲线 Mannheim曲线 |
Applications of tubular surfaces in theory of curves |
| |
| Su Nong,Liu Ling.Applications of tubular surfaces in theory of curves[J].Pure and Applied Mathematics,2012(1):67-72. |
| |
| Authors: | Su Nong Liu Ling |
| |
| Institution: | (Department of Mathematics,Beijing Information Science and Technology University,Beijing 100192,China) |
| |
| Abstract: | This paper studies the lines of curvature,asymptotic curves and geodesics on a tubular surface around a smooth curve,provides their equations and shows the relations between these lines and Bertrand-curve or a Mannheim-curve.Another proofs of the suffcient and necessary conditions of a curve to be a Bertrand-curve or a Mannheim-curve are given.As a further result,the relation of the curvature and the torsion of a Mannheim mate is also obtained. |
| |
| Keywords: | tubular surface asymptote geodesic bertrand-curve mannheim-curve |
| 本文献已被 CNKI 等数据库收录！ |
