Algebraic & Geometric Topology

On real analytic orbifolds and Riemannian metrics

Marja Kankaanrinta

Full-text: Open access

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

Permanent link to this document
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

Keywords
orbifold real analytic complete Riemannian metric frame bundle

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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