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

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.