Two Proof Methods and Applications to Equalities Concerning Gauge Matrix and Bending Matrix
Fang Li-jing · Journal of Guangxi University for Nationalities · 2011
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).