等距对应视角下正螺面上渐近线的研究  

Study of Asymptotes on Positive Spiral Surface Based on Isometric Correspondence

作　　者：王新璇 包图雅[1] 张宇[1] WANG Xinxuan;BAO Tuya;ZHANG Yu(College of Mathematical Sciences,Inner Mongolia Minzu University,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2024年第1期83-90,共8页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金项目(11661062);内蒙古自治区自然科学基金项目(2022MS01015);内蒙古自治区高等学校青年科技英才支持计划项目(NJYT-19-A09)。

摘　　要：为了得到正螺面上渐近线等距对应到悬链面上像曲线的性质,根据正螺面上渐近线成为测地线的条件,将正螺面上渐近线是否为测地线分类讨论,利用正螺面与悬链面之间的等距对应关系,对悬链面上像曲线进行研究,并计算了悬链面上像曲线的测地曲率与法曲率之间的关系以及测地挠率与法曲率之间的关系。To obtain the property that the asymptotes on the positive spiral plane under the isometric correspon⁃dence to the image curve on the catenary surface,according to the condition that the asymptotes on the positive spi⁃ral plane become geodesics,the classification of whether the asymptotes on the positive spiral plane are geodesics is discussed.The image curves on the catenary surface are studied by utilizing the isometric correspondence between the positive spiral surface and the catenary surface,and working out the relationships between the ratios of the geo⁃desic curvature and normal curvature,between the ratios of the geodesic torsion and normal curvature,of the image curves on the catenary surface.

关 键 词：正螺面 等距对应 渐近线 法曲率 

分 类 号：O186.11[理学—数学]