Solving Local Equivalence Problems with the Equivariant Moving Frame Method

Symmetry Integrability and Geometry-Methods and Applications

article

Francis Valiquette¹ 

[1] Department of Mathematics and Statistics, Dalhousie University

关键词: dif ferential invariant;    equivalence problem;    Maurer–Cartan form;    moving frame;   

DOI  :  10.3842/SIGMA.2013.029

来源: National Academy of Science of Ukraine

【 摘 要 】

Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications and assumptions, the equivariant moving frame constructions extend to submanifold jets where the pseudo-group does not act freely at any order. Once this is done, we review the solution to the local equivalence problem of submanifolds within the equivariant moving frame framework. This offers an alternative approach to Cartan's equivalence method based on the theory of G -structures.

【 授权许可】

Unknown