Abstract
AbstractWe characterize Riemannian orbifolds with an upper curvature bound in the Alexandrov sense as reflectofolds, i.e., Riemannian orbifolds all of whose local groups are generated by reflections, with the same upper bound on the sectional curvature. Combined with a result by Lytchak–Thorbergsson this implies that a quotient of a Riemannian manifold by a closed group of isometries has locally bounded curvature (from above) in the Alexandrov sense if and only if it is a reflectofold.
Funder
Ludwig-Maximilians-Universität München
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Alexander, S., Kapovitch, V., Petrunin, A.: An invitation to Alexandrov geometry. CAT(0) spaces. Springer Briefs in Mathematics. Springer, Cham, xii+88 pp. (2019)
2. Alexandrino, M., Bettiol, R.: Lie groups and geometric aspects of isometric actions. Springer, Cham. x+213 pp. (2015)
3. Alexandrov, A.D.: A theorem on triangles in a metric space and some of its applications. (Russian) Trudy Mat. Inst. Steklov. 38, 5–23.Izdat. Akad. Nauk SSSR, Moscow. (1951)
4. Berestovskij, V.N., Nikolaev, I.G.: Multidimensional generalized Riemannian spaces. Geometry, IV, 165–243, 245–250, Encyclopaedia Math. Sci., 70, Springer, Berlin, (1993)
5. Bridson, M.R., Haefliger, A.: Metric spaces of non-positive curvature. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319. Springer-Verlag, Berlin, xxii+643 pp. (1999)