## Algebraic & Geometric Topology

### On real analytic orbifolds and Riemannian metrics

Marja Kankaanrinta

#### Abstract

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

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

Dates
Accepted: 17 March 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715643

Digital Object Identifier
doi:10.2140/agt.2013.13.2369

Mathematical Reviews number (MathSciNet)
MR3073921

Zentralblatt MATH identifier
1275.57038

Subjects
Primary: 57R18: Topology and geometry of orbifolds

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715643

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