# nLab Cartan geometry

### Context

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

Cartan geometry is a common generalization of Riemannian geometry, conformal geometry and Klein geometry, which generalizes the linear tangent spaces of the former to the more general homogeneous spaces of the latter.

Intuitively, Cartan geometry studies the geometry of a manifold by ‘rolling’ another manifold, the ‘model geometry’ on it. The model geometry may be any Klein geometry.

## References

A standard textbook is

• R. Sharpe, Differential Geometry – Cartan’s Generalization of Klein’s Erlagen program Springer (1997)