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arXiv · 1303.5925

Strongly exponential symmetric spaces

Yannick Voglaire
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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.

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Yannick Voglaire. 2014-04-06. Strongly exponential symmetric spaces. https://doi.org/10.1093/imrn%2Frnt149

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