摘要
首先着力阐明,唯独二阶反对称张量Ω才存在着它唯一的对偶矢ω.后者一经找到,立刻可见其表达式实际上就是"ω与Ω之间关系",亦即本文正向关系问题之解.接着处理反向关系问题,又求得我们也想要找的"Ω与ω之间关系".综合以上二结果,便导致总结论——本工作之成果汇总.另外,文末附带将Lurie[2]给出的,同时反映上述Ω与ω两者特征的一对公式作了推广.
Firstly,make certain that as to an antisymmetric tensor Ω of order two,there exists exactly one corresponding vector ω,known as the dual vector of Ω. Once the latter has been found,we see that its expression is just the relation between ω and Ω,i.e.,the solution for the positive-way problem. Next,let us treat the negativeway problem so as to get the relation between Ω and ω. Synthesizing both results above,we are led to the general conclusion. In addition,a pair of formulas given by Lurie,which reflect simultaneously the features of both Ω andω,are generalized at the end of this paper.
出处
《高等数学研究》
2016年第1期31-34,共4页
Studies in College Mathematics
关键词
二阶反对称张量
对偶矢
总结论
Lurie公式之推广
antisymmetric tensor of order two
dual vector
general conclusion
generalization of the Lurie formulas
