Orbifolds of Maximal Diameter
نویسنده
چکیده
In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n− 1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (S, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) acting discontinuously and isometrically on S. It is also shown that the singular locus of the orbifold forms a geometric barrier to the length minimization property of geodesics. We also extend the Bishop relative volume comparison theorem to Riemannian orbifolds.
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