Riemannian metrics on Lie groupoids

Matias Del Hoyo, Rui Loja Fernandes

Research output: Contribution to journalArticlepeer-review


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 allows 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.

Original languageEnglish (US)
Pages (from-to)143-173
Number of pages31
JournalJournal fur die Reine und Angewandte Mathematik
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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