Editing Clifford–Klein form (section)

==History==
According to [[Moritz Epple]], the Clifford-Klein forms began when [[W. K. Clifford]] used [[quaternion]]s to ''twist'' their space. "Every twist possessed a space-filling family of invariant lines", the [[Clifford parallel]]s. They formed "a particular structure embedded in elliptic 3-space", the [[Clifford surface]], which demonstrated that "the same local geometry may be tied to spaces that are globally different." [[Wilhelm Killing]] thought that for free mobility of rigid bodies there are four spaces: Euclidean, hyperbolic, elliptic and spherical. They are spaces of [[constant curvature]] but constant curvature differs from free mobility: it is local, the other is both local and global. Killing's contribution to Clifford-Klein space forms involved formulation in terms of [[group (mathematics)|group]]s, finding new classes of examples, and consideration of the scientific relevance of spaces of constant curvature. He took  up  the task to develop physical theories of CK space forms. [[Karl Schwarzchild]] wrote “The admissible measure of the curvature of space”, and noted in an appendix that physical space may actually be a non-standard space of constant curvature.