相似几何中的活动标架  

Moving Frames in Similarity Geometry

作　　者：李艳艳[1] 

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000

出　　处：《河南科学》2013年第12期2121-2125,共5页Henan Science

基　　金：国家青年自然科学基金(11101332);陕西省教育厅自然科学基金(2010JK893);咸阳师范学院自然科学基金(11XSYK201)

摘　　要：利用Fels和Olver的活动标架法,探讨2维和3维相似几何中曲线的具体活动标架和微分不变量.得到了2维和3维相似几何中曲线的微分不变量在局部坐标下的具体形式,相应的Frenet标架和公式.活动标架法提供了研究相似几何在相似变换群作用下的几何性质的方法.Using Fels and Olver＇s method of moving frames, the author discussed the specific moving frames and differential invariants for curves in two-dimensional and three-dimensional similarity geometries. The specific forms of differential invariants for curves under local coordinates, the associated Frenet frames and Frenet formulae in two- dimensional and three-dimensional similarity geometries were obtained. The method of moving frames provide a method for studing the geometric properties of similarity geometry under the action of similarity transformation group.

关 键 词：活动标架法 相似几何 微分不变量 

分 类 号：O175.2[理学—数学]