Conformal connection

In conformal differential geometry, a conformal connection is a Cartan connection on an n-dimensional manifold M arising as a deformation of the Klein geometry given by the celestial n-sphere, viewed as the homogeneous space

where P is the stabilizer of a fixed null line through the origin in Rⁿ⁺², in the orthochronous Lorentz group O⁺(n+1,1) in n+2 dimensions.

Any manifold equipped with a conformal structure has a canonical conformal connection called the normal Cartan connection.

A conformal connection on an n-manifold M is a Cartan geometry modelled on the conformal sphere, where the latter is viewed as a homogeneous space for O⁺(n+1,1). In other words it is an O⁺(n+1,1)-bundle equipped with

such that the solder form induced by these data is an isomorphism.

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