Geodesic
On real analytic orbifolds and Riemannian metrics
Kankaanrinta, Marja1
1Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville, VA 22903, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2369-2381
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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.

DOI : 10.2140/agt.2013.13.2369
Classification : 57R18
Keywords: orbifold, real analytic, complete Riemannian metric, frame bundle

Kankaanrinta, Marja  1

1 Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville, VA 22903, USA 
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Kankaanrinta, Marja. On real analytic orbifolds and Riemannian metrics. Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2369-2381. doi: 10.2140/agt.2013.13.2369

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