zbMATH — the first resource for mathematics

Orbifolds of maximal diameter. (English) Zbl 0801.53031
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 \(= \pi\), must have constant sectional curvature 1, and must be a quotient of the sphere (\(S^ n\),can) of constant sectional curvature 1 by a subgroup of the orthogonal group \(\mathbb{O}(n+1)\) acting discontinuously and isometrically on \(S^ n\). 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.

53C20 Global Riemannian geometry, including pinching
Full Text: DOI