Spherical space form

A spherical space form is a quotient of the n-dimensional sphere S^n by a finite group of isometries acting freely — that is, without fixed points. In three dimensions, these are the manifolds that admit spherical geometry, one of the eight geometries in the geometrization program. The classification of 3-dimensional spherical space forms, completed by Wolf and others, connects finite group theory to Riemannian geometry in a remarkably rigid way: the geometry is entirely determined by the group's action, and the resulting manifolds are among the few that admit positive Ricci curvature in dimension three.