Strongly exponential symmetric spaces
Differential Geometry
2015-07-27 v2 Mathematical Physics
math.MP
Abstract
We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a geometric characterization of the (strongly) exponential solvable symmetric spaces as those spaces for which every triangle admits a unique double triangle. This work is motivated by Weinstein's quantization by groupoids program applied to symmetric spaces.
Cite
@article{arxiv.1303.5925,
title = {Strongly exponential symmetric spaces},
author = {Yannick Voglaire},
journal= {arXiv preprint arXiv:1303.5925},
year = {2015}
}
Comments
Some corrections and typos. To appear in International Mathematics Research Notices