广西民族大学学报:自然科学版
廣西民族大學學報:自然科學版
엄서민족대학학보:자연과학판
Journal of Guangxi University For Nationalities(Natural Science Edition)
2011年
2期
49-55
,共7页
度量矩阵(gij)%弯曲矩阵(bij)%代数证法%简捷的几何证法%Weingarten映射%渐近曲线的挠率
度量矩陣(gij)%彎麯矩陣(bij)%代數證法%簡捷的幾何證法%Weingarten映射%漸近麯線的撓率
도량구진(gij)%만곡구진(bij)%대수증법%간첩적궤하증법%Weingarten영사%점근곡선적뇨솔
gauge matrix%bending matrix%algebraic proof%geometric proof%Weingarten mapping%torsion of an asymptotic curve
给出了度量矩阵(gij)和弯曲矩阵(bij)的关系等式(4)与(5)(见文章第2节)的代数证法和几何证法,其中几何证法回避了抽象的Weingarten映射,更适合众多微分几何初学者.简明快捷的几何证法不但揭示了等式(4)的几何含义,而且给出等式(4)与(5)在几何上的应用实例.
給齣瞭度量矩陣(gij)和彎麯矩陣(bij)的關繫等式(4)與(5)(見文章第2節)的代數證法和幾何證法,其中幾何證法迴避瞭抽象的Weingarten映射,更適閤衆多微分幾何初學者.簡明快捷的幾何證法不但揭示瞭等式(4)的幾何含義,而且給齣等式(4)與(5)在幾何上的應用實例.
급출료도량구진(gij)화만곡구진(bij)적관계등식(4)여(5)(견문장제2절)적대수증법화궤하증법,기중궤하증법회피료추상적Weingarten영사,경괄합음다미분궤하초학자.간명쾌첩적궤하증법불단게시료등식(4)적궤하함의,이차급출등식(4)여(5)재궤하상적응용실례.
As for Equalities (4) and (5), which concern Gauge Matrix and bending Matrix, we give an algebraic method and a geometric method to prove them, respectively. These two proof methods all have fairly high technique. In particular, the geometric method slides over the concept of Weingarten mapping such that this way fits a throng of novices in Differential Geometry. Also, we dig up the geometric implication contained in Equality (4) by geometric method with concise and shortcut trait. Moreover, we give two examples to elaborate geometric applications of Equalities (4) and (5).