Algebraic & Geometric Topology

On real analytic orbifolds and Riemannian metrics

Marja Kankaanrinta

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We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozeki concerning Riemannian metrics on manifolds to the orbifold setting: Let X be a smooth (real analytic) orbifold and let α be a smooth (real analytic) Riemannian metric on X. Then X has a complete smooth (real analytic) Riemannian metric conformal to α.

Article information

Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2369-2381.

Received: 3 December 2012
Accepted: 17 March 2013
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 57R18: Topology and geometry of orbifolds

orbifold real analytic complete Riemannian metric frame bundle


Kankaanrinta, Marja. On real analytic orbifolds and Riemannian metrics. Algebr. Geom. Topol. 13 (2013), no. 4, 2369--2381. doi:10.2140/agt.2013.13.2369.

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