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 be a smooth (real analytic) orbifold and let be a smooth (real analytic) Riemannian metric on . Then has a complete smooth (real analytic) Riemannian metric conformal to .
Citation
Marja Kankaanrinta. "On real analytic orbifolds and Riemannian metrics." Algebr. Geom. Topol. 13 (4) 2369 - 2381, 2013. https://doi.org/10.2140/agt.2013.13.2369
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