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
- O+(n+1,1)/P
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.
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“One must always maintain one’s connection to the past and yet ceaselessly pull away from it. To remain in touch with the past requires a love of memory. To remain in touch with the past requires a constant imaginative effort.”
—Gaston Bachelard (1884–1962)