相似空间中不变的欧拉-拉格朗日方程

Invariant Euler-Lagrange Equation in Similarity Space

利用Fels和Olver的等变活动标架法及Kogan和Olver的诱导的不变变分二重复形对3维相似几何中曲线微分不变量的不变变分问题进行了研究.给出了3维相似几何中相似变换群的延拓无穷小生成子,得出了3维相似几何中曲线微分不变量的变分所对应的具体的欧拉-拉格朗日方程.

Invariant variational problem for differential invariants of curves in three-dimensional similarity geometry is studied using Fels and Olver＇s equivariant moving frame method and Kogan and Olver＇s induced invariant variational bicomplex.The prolonged infinitesimal generators of similarity transformation in three-dimensional similarity geometry are given.The concrete Euler-Lagrange equation corresponding to invariant variational problem for differential invariants of curves in three-dimensional similarity geometry is obtained.