derived smooth geometry
Klein geometries form the local models for Cartan geometries.
A Klein geometry is a pair where is a Lie group and is a closed Lie subgroup of such that the (left) coset space is connected. acts transitively on the homogeneous space . We may think of as the stabilizer of a point in .
|local model||global geometry|
|Klein geometry||Cartan geometry|
|Klein 2-geometry||Cartan 2-geometry|
|higher Klein geometry||higher Cartan geometry|
The notion of Klein geometry goes back to articles such as
in the context of what came to be known as the Erlangen program.
A review is for instance in