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Invariant theory for conformal and CR geometry. (English) Zbl 0814.53017
The authors study invariants for conformal and CR-differential geometry, in analogy to Riemannian and affine differential geometry. The following results are given. In the conformal case, every even invariant of \({\mathcal H}_ k\) is a Weyl invariant; there are no nonzero odd invariants of degree \(d < n\); every nonzero odd invariant of degree \(d = n\) is exceptional; all odd invariants of degree \(d > n\) are Weyl invariants. For curvature tensors, every even invariant of \({\mathcal K}\) is a Weyl invariant; there are no nonzero odd invariants of degree \(d < {n \over 2}\); every nonzero odd invariant of degree \(d = {n \over 2}\) is exceptional; all odd invariants of degree \(d > {n \over 2}\) are Weyl invariants. In the CR case, all invariants of \({\mathcal H}_ k\) are Weyl invariants. There are two steps in the description of the invariants. First, the space of jets of the structures modulo the action of formal diffeomorphisms is represented. In the second step, invariants are produced by “complete contractions”, and it is to be determined whether every invariant arises this way (below the order of obstruction in the CR and the even-dimensional conformal cases).

MSC:
53A55 Differential invariants (local theory), geometric objects
32V99 CR manifolds
53A30 Conformal differential geometry (MSC2010)
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