English

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.

Keywords

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

R2 v1 2026-06-21T23:47:16.445Z