Riemannian metrics on differentiable stacks

Matias del Hoyo, Rui Loja Fernandes

Research output: Contribution to journalArticlepeer-review


We study Riemannian metrics on Lie groupoids in the relative setting. We show that any split fibration between proper groupoids can be made Riemannian, and we use these metrics to linearize proper groupoid fibrations. As an application, we derive rigidity theorems for Lie groupoids, which unify, simplify and improve similar results for classic geometries. Then we establish the Morita invariance for our metrics, introduce a notion for metrics on stacks, and use them to construct stacky tubular neighborhoods and to prove a stacky Ehresmann theorem.

Original languageEnglish (US)
Pages (from-to)103-132
Number of pages30
JournalMathematische Zeitschrift
Issue number1-2
StatePublished - Jun 1 2019

ASJC Scopus subject areas

  • Mathematics(all)

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