  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 $\alpha$ be a
smooth (real analytic) Riemannian metric on $X$. Then $X$ has a complete smooth
(real analytic) Riemannian metric conformal to $\alpha$.
