On real analytic orbifolds and Riemannian metrics

Kankaanrinta, Marja

doi:10.2140/agt.2013.13.2369

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On real analytic orbifolds and Riemannian metrics

Marja Kankaanrinta

Algebraic & Geometric Topology 13 (2013) 2369–2381

DOI: 10.2140/agt.2013.13.2369

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 $α$ .

Keywords

orbifold, real analytic, complete Riemannian metric, frame bundle

Mathematical Subject Classification 2010

Primary: 57R18

References

Publication

Received: 3 December 2012

Accepted: 17 March 2013

Published: 2 July 2013

Authors

Marja Kankaanrinta
Department of Mathematics University of Virginia PO Box 400137 Charlottesville, VA 22903 USA

Volume 13, issue 4 (2013)