Riemannian metrics on Lie groupoids

By Matías L. del Hoyo, Rui Loja Fernandes. 2014

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We introduce a notion of metric on a Lie groupoid, compatible with multipli- cation, 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cadd95145ca40c9a5c905cf92de44045943ab554