scholarly journals Correction: Bates et al. Vector Fields and Differential Forms on the Orbit Space of a Proper Action. Axioms 2021, 10, 118

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 173
Author(s):  
Larry Bates ◽  
Richard Cushman ◽  
Jędrzej Śniatycki
Keyword(s):  
Vector Fields ◽  
Differential Forms ◽  
Orbit Space ◽  
Proper Action

There was an error in the original article [...]

scholarly journals Vector Fields and Differential Forms on the Orbit Space of a Proper Action

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 118
Author(s):  
Larry Bates ◽  
Richard Cushman ◽  
Jędrzej Śniatycki
Keyword(s):  
Lie Group ◽  
Smooth Manifold ◽  
Vector Fields ◽  
Differential Forms ◽  
Orbit Space ◽  
Proper Action ◽  
Multilinear Maps

In this paper, we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This yields an intrinsic view of vector fields and differential forms on the orbit space.

Modules of vector fields, differential forms and degenerations of differential systems

1996 ◽  
Vol 95 (1) ◽  
pp. 411-428 ◽  
Author(s):  
P. Mormul ◽  
M. Zhitomirskii
Keyword(s):  
Vector Fields ◽  
Differential Forms ◽  
Differential Systems

Differential geometry

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Differential Geometry ◽  
Vector Fields ◽  
Differential Forms ◽  
Curvilinear Coordinates ◽  
Moving Frames ◽  
Tensor Fields ◽  
Metric Tensor ◽  
Vector Calculus ◽  
Vector Version ◽  
Definition Of

This chapter presents some elements of differential geometry, the ‘vector’ version of Euclidean geometry in curvilinear coordinates. In doing so, it provides an intrinsic definition of the covariant derivative and establishes a relation between the moving frames attached to a trajectory introduced in Chapter 2 and the moving frames of Cartan associated with curvilinear coordinates. It illustrates a differential framework based on formulas drawn from Chapter 2, before discussing cotangent spaces and differential forms. The chapter then turns to the metric tensor, triads, and frame fields as well as vector fields, form fields, and tensor fields. Finally, it performs some vector calculus.

Manifolds, Vector Fields, and Differential Forms

1999 ◽  
pp. 121-146 ◽  
Author(s):  
Jerrold E. Marsden ◽  
Tudor S. Ratiu
Keyword(s):  
Vector Fields ◽  
Differential Forms

Interlude: Manifolds, Vector Fields, and Differential Forms

1994 ◽  
pp. 109-129
Author(s):  
Jerrold E. Marsden ◽  
Tudor S. Ratiu
Keyword(s):  
Vector Fields ◽  
Differential Forms

Differential forms and vector fields with a manifold of singular points

1993 ◽  
Vol 5 (12) ◽  
Author(s):  
Michail Zhitomirskii
Keyword(s):  
Vector Fields ◽  
Differential Forms ◽  
Singular Points
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