Geometry of infinite dimensional Cartan Developments
Differential Geometry
2024-08-13 v2 Functional Analysis
Abstract
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold to a smooth mapping from into the Lie group. In this paper this is generalized to infinite dimensional 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.
Cite
@article{arxiv.2404.05416,
title = {Geometry of infinite dimensional Cartan Developments},
author = {Johanna Michor and Peter W. Michor},
journal= {arXiv preprint arXiv:2404.05416},
year = {2024}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:math/0609077, arXiv:math/9801007