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On real analytic orbifolds and Riemannian metrics

Marja Kankaanrinta

Algebraic & Geometric Topology 13 (2013) 2369–2381

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.

orbifold, real analytic, complete Riemannian metric, frame bundle
Mathematical Subject Classification 2010
Primary: 57R18
Received: 3 December 2012
Accepted: 17 March 2013
Published: 2 July 2013
Marja Kankaanrinta
Department of Mathematics
University of Virginia
PO Box 400137
Charlottesville, VA 22903