Moving coframes: I. A practical algorithm

被引：184

作者：

Fels, M ^{[1
]}

Olver, PJ ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

ACTA APPLICANDAE MATHEMATICAE | 1998年 / 51卷 / 02期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

moving frame; differential invariant; Lie group; Lie pseudogroup; equivalence; symmetry; computer vision;

D O I：

10.1023/A:1005878210297

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is the first in a series of papers devoted to the development and applications of a new general theory of moving frames. In this paper, we formulate a practical and easy to implement explicit method to compute moving frames, invariant differential forms, differential invariants and invariant differential operators, and solve general equivalence problems for both finite-dimensional Lie group actions and infinite Lie pseudo-groups. A wide variety of applications, ranging from differential equations to differential geometry to computer vision are presented. The theoretical justifications for the moving coframe algorithm will appear in the next paper in this series.

引用

页码：161 / 213

页数：53