English

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 MM to a smooth mapping from MM into the Lie group. In this paper this is generalized to infinite dimensional MM 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.

Keywords

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

R2 v1 2026-06-28T15:47:22.820Z