Geometries of orthogonal groups and their contractions: a unified classical deformation viewpoint

The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of their spaces is also advanced.Comment: 9 pages, LaTeX; contribution presented by M.Santander to the II International Workshop on Classical and Quantum Integrible Systems (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phys.