几何教学中讲授伪欧氏空间中曲线几何性质探究  

The Explore of Adding Some Geometrical Properties of Curves in Pseudo Euclidean Space During Geometry Teaching

作　　者：张会娜 孙建国 常丽[2] ZHANG Hui-na;SUN Jian-guo;CHANG Li(School of Science, China University of Petroleum （east China）, Qingdao 266580, China;Henan College of Transportation, Faculty of Basic Science, Zhengzhou 451000, China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580 [2]河南交通职业技术学院基础教育部,河南郑州451000

出　　处：《数学的实践与认识》2018年第8期284-289,共6页Mathematics in Practice and Theory

基　　金：中国石油大学(华东)重点教改项目-常规教学研究与改革重点项目(JY-A201617);中国石油大学(华东)青年教改一般项目(QN201530);中央高校基本科研专项资金资助(17CX02049)

摘　　要：曲线,曲面理论是古典微分几何教学中的主要研究对象.然而在古典微分几何的教学中,学生往往只是知道如何解题,不知道微分几何学的主要研究工具,以至于不会运用微分几何解决后继课程中的问题.因此在微分几何的教学中有必要增加一些伪欧氏空间中曲线理论.首先讨论在教学中的一个非常重要曲线理论研究工具-费雷内标架,其次运用该标架讨论在四维伪欧氏空间中斜螺线的一些几何性质,最后通过横截性原理与开折理论,结合微分几何基础给出了由偏零斜螺线生成的密切超曲面的局部几何性质.The theories of curves and surfaces are the most important in the teaching of differential geometry. However, in the classical differential geometry teaching, students often only know how to solve, do not know the main research tool in differential geometry, so as not to use differential geometry solve problems in the subsequent course. Therefore, in the teaching of differential geometry, it is necessary to increase the theory of curves in pseudo Euclidean space. In this paper we first discuss in teaching is a very important tool- Ferene frame, then use the frame to discuss some geometric properties of some slant helix in pseudo Euclidean space. Finally, the local geometric properties of hypersurfaces generated by slant helix are given by combining the principle of truncation and the theory of unfolding with differential geometry.

关 键 词：微分几何 斜螺线 伪欧氏空间 密切超曲面 

分 类 号：G642[文化科学—高等教育学] O186.1-4[文化科学—教育学]