Results 1 
5 of
5
Solving local equivalence problems with the equivariant moving frame method
"... Abstract. Given a Lie pseudogroup 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 mod ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Given a Lie pseudogroup 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 pseudogroup 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 Gstructures. Key words: differential invariant; equivalence problem; Maurer–Cartan form; moving frame
Symmetry, Integrability and Geometry: Methods and Applications Solving Local Equivalence Problems with the Equivariant Moving Frame Method ⋆
"... Abstract. Given a Lie pseudogroup 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 modi ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Given a Lie pseudogroup 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 pseudogroup 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 Gstructures. Key words: differential invariant; equivalence problem; Maurer–Cartan form; moving frame 2010 Mathematics Subject Classification: 53A55; 58A15
Point Equivalence of SecondOrder ODEs: Maximal Invariant Classification Order
"... ar ..."
(Show Context)
Invariants of objects and their images under surjective maps
, 2015
"... Abstract: We examine the relationships between the differential invariants of objects and of their images under a surjective maps. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of th ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: We examine the relationships between the differential invariants of objects and of their images under a surjective maps. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably. In the former case, we establish a constructible isomorphism between the algebra of differential invariants of the images and the algebra of fiberwise constant (gauge) differential invariants of the objects. In the latter case, we describe residual effects of the full transformation group on the image invariants. Our motivation comes from the problem of reconstruction of an object from multipleview images, with central and parallel projections of curves from threedimensional space to the twodimensional plane serving as our main examples. 1 Introduction. The subject of this paper is the behavior of invariants and, particularly, differential invariants under surjective maps. While our theoretical results are valid for manifolds of arbitrary dimension, the motivating examples are central and parallel projections from threedimensional space onto the twodimensional plane, as prescribed by simple cameras. We concentrate on