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Geometry of infinite dimensional Cartan developments
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The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer–Cartan equation on a simply connected manifold [Formula: see text] to a smooth mapping from [Formula: see text] into the Lie group. In this paper, this is generalized to infinite dimensional [Formula: see text] for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development.
Title: Geometry of infinite dimensional Cartan developments
Description:
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer–Cartan equation on a simply connected manifold [Formula: see text] to a smooth mapping from [Formula: see text] into the Lie group.
In this paper, this is generalized to infinite dimensional [Formula: see text] for infinite dimensional regular Lie groups.
The Cartan development is viewed as a generalization of the evolution map of a regular Lie group.
The tangent mapping of a Cartan development is identified as another Cartan development.
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