Invariant Differential Operator - Conformal Invariance

Conformal Invariance

• The sphere (here shown as a red circle) as a conformal homogeneous manifold.

Given a metric

on, we can write the sphere as the space of generators of the nill cone

In this way, the flat model of conformal geometry is the sphere with and P the stabilizer of a point in . A classification of all linear conformally invariant differential operators on the sphere is known (Eastwood and Rice, 1987).