吉首大学学报（自然科学版） ›› 2021, Vol. 42 ›› Issue (3): 13-20.DOI: 10.13438/j.cnki.jdzk.2021.03.003
• 数学 • 上一篇 下一篇
安佰玲，张德燕
出版日期:
发布日期:
作者简介:
基金资助:
AN Bailing, ZHANG Deyan
Online:
Published:
摘要：先通过抛物线的参数方程给出了二次曲面存在抛物截面的必要条件和充分条件，再结合抛物线的投影方程及其不变量，分别给出了二次曲面存在平行于坐标面、平行于z轴及与z轴相交的抛物截面的充要条件.利用这些结果，讨论了5种典型二次曲面抛物截面的存在性问题.
关键词： 二次曲面, 抛物线, 抛物截面, 不变量, 方程, 存在性
Abstract: First, the necessary and sufficient conditions for the existence of parabolic section of a quadratic surface are given according to the parameter equation of the parabola. Secondly, the necessary and sufficient conditions for the existence of parabolic sections, which are parallel to the coordinate plane and the z-axis and intersecting with the z-axis, are given respectively with combining the projection equations of the parabola and its invariant. Finally, the existence problem for parabolic sections of five typical quadratic surfaces is discussed.
Key words: quadratic surface, parabola, parabolic section, invariant, equation, existence
安佰玲, 张德燕. 二次曲面抛物截面存在性定理[J]. 吉首大学学报（自然科学版）, 2021, 42(3): 13-20.
AN Bailing, ZHANG Deyan. Existence Theorems for Parabolic Sections of Quadratic Surface[J]. Journal of Jishou University(Natural Sciences Edition), 2021, 42(3): 13-20.
0 / / 推荐
导出引用管理器 EndNote|Ris|BibTeX
链接本文: https://zkxb.jsu.edu.cn/CN/10.13438/j.cnki.jdzk.2021.03.003
https://zkxb.jsu.edu.cn/CN/Y2021/V42/I3/13
