Heisenberg群上球面曲线的渐屈线的奇点  

Singularities for Evolutes of Spherical Curves in Heisenberg Group

作　　者：苗佳晶 刘海明 MIAO Jia-jing;LIU Hai-ming(School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang 157011, China)

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157011

出　　处：《数学的实践与认识》2017年第21期284-290,共7页Mathematics in Practice and Theory

基　　金：牡丹江师范学院省级重点创新预研项目(SY201320)

摘　　要：3维Heisenberg群H_3是具有4维等距群的齐性流形,是除了空间形式之外最简单的3维流形之一,而且从代数观点来看,H_3是二阶幂零李群.主要从奇点理论的视角考察3维Heisenberg群上球面曲线的渐屈线的奇异性质,主要结果表明这类渐屈线可以被视作焦曲线并且局部上微分同胚于一般尖点.The three dimensional Heisenberg group H3 is a three dimensional homogeneous manifold with a 4-dimensional isometry group; hence it is the most simple 3-manifold apart from the space-forms, it is the two-step nilpotent Lie group from the view point of algebra. In this paper, we consider the singular properties of evolutes for spherical curves in Heisenberg group, the main result indicates that this kind of evolute can be seen as caustic and it is locally diffeomorphic to ordinary cusp.

关 键 词：HEISENBERG群 球面曲线 渐屈线 一般尖点 

分 类 号：O152[理学—数学]