Riemannian metrics on Lie groupoids
Differential Geometry
2018-04-03 v2
Abstract
We introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allow us to establish a Linearization Theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of the Weinstein-Zung Linearization Theorem for proper Lie groupoids. This new notion of metric has a simplicial nature which will be explored in future papers of this series.
Cite
@article{arxiv.1404.5989,
title = {Riemannian metrics on Lie groupoids},
author = {Matias L. del Hoyo and Rui Loja Fernandes},
journal= {arXiv preprint arXiv:1404.5989},
year = {2018}
}
Comments
29 pages; Final version accepted for publication in Journal f\"ur die reine und angewandte Mathematik (Crelle)