Group contraction and the nine Cayley-Klein geometries

A one-to-one correspondence between the nine Cayley-Klein geometries and the so-called kinematic groups is presented. As is well known, the kinematic groups are related to each other through group contraction. The pattern of contraction is explained by relating each kinematic group to a specific Cayley-Klein geometry. The very meaning of group contraction is deeply rooted in the relationship between the nine geometries. Lie algebras of those geometries are explicitly constructed.In part from the Tesina de LicenciaturaM. A. Fernandez Sanjuan, Tesina de Licenciatura: Contracciones anisötropas del grupo de Poincar, Universidad de Valladolid, 1981.