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Mathematics > Differential Geometry

arXiv:1404.5989 (math)
[Submitted on 23 Apr 2014 (v1), last revised 11 Feb 2015 (this version, v2)]

Title:Riemannian metrics on Lie groupoids

Authors:Matias L. del Hoyo, Rui Loja Fernandes
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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.
Comments: 29 pages; Final version accepted for publication in Journal für die reine und angewandte Mathematik (Crelle)
Subjects: Differential Geometry (math.DG)
MSC classes: 22A22, 58H05
Cite as: arXiv:1404.5989 [math.DG]
  (or arXiv:1404.5989v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1404.5989
Journal reference: Journal fur die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 735, Pages 143-173
Related DOI: https://doi.org/10.1515/crelle-2015-0018

Submission history

From: Rui Loja Fernandes [view email]
[v1] Wed, 23 Apr 2014 21:34:25 UTC (36 KB)
[v2] Wed, 11 Feb 2015 17:54:30 UTC (38 KB)
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