Title:
Cartan geometries
Abstract:
Cartan geometries provide a description of manifolds that carry certain types of geometric structures as "curved analogs" of homogeneous spaces. My talk will start by outlining this concept and its role in connecting classical geometry, in particular Klein's Erlangen program, to differential geometry. Next, I will briefly discuss examples for which the concept is of interest. Finally, I will sketch an application of this point of view to the study of automorphism groups of geometric structures.