曲面(曲线)关于另一曲面(曲线)的对称性研究  

Research on the Symmetry of Surface(Curve)about Another Surface(Curve)

作　　者：杨成[1] 周世武 汤建钢 Yang Cheng;Zhou Shiwu;Tang Jiangang(Civil Aviation Flight University of China,Guanghan,Sichuan 618300,China;College of Mathematics and Statistics,Yili Normal University,Yining,Xinjiang 835000,China)

机构地区：[1]中国民航飞行学院,四川广汉618300 [2]伊犁师范大学数学与统计学院,新疆伊宁835000

出　　处：《伊犁师范大学学报（自然科学版）》2022年第2期1-14,共14页Journal of Yili Normal University：Natural Science Edition

基　　金：新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2019I024).

摘　　要：首先定义曲面Σ_(1)关于另一曲面Σ的H-投影和qλ-对称像(简称(qλ-sy)像),并讨论了曲面Σ_(1)关于曲面Σ的H-投影的有关性质,得到了定理2.2、定理2.3和定理2.4;然后讨论曲面Σ_(1)关于曲面Σ的(qλ-sy)像(记为Σ_(2)),它就是曲面Σ_(1)关于曲面Σ_(2)的H-投影,得到了定理3.3、定理3.4、定理3.5;最后讨论了有关弧长、面积和体积的计算.Firstly,the H-projection andqλ-symmetric images(referred toas(qλ-sy)images)of surfaceΣ_(1) with respectto another surfaceΣare defined,and somepropertiesoftheH-projection ofsurfaceΣ_(1) with respecttosurfaceΣare discussed.Theorem 2.2,Theorem 2.3 and Theorem 2.4 are obtained.Then,we discussthe(qλ-sy)image(denoted asΣ_(2)) of surfaceΣ_(1) with respect to surfaceΣ,and obtaintheorem 3.3,theorem 3.4 and theorem 3.5.Finally,the calculationofarclength,area andvolumeis discussed.

关 键 词：曲面 对称性 投影 

分 类 号：O159[理学—数学] O154.1[理学—基础数学]