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Conformal transformation, conformal change, and conformal covariants. (English) Zbl 0678.53025
Proc. Winter Sch. Geom. Phys., SrnĂ­/Czech. 1988, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 21, 115-134 (1989).
[For the entire collection see Zbl 0672.00006.]
The author studies differential operators covariant under conformal changes of metrics on Riemannian or pseudo-Riemannian manifolds of various dimensions with particular emphasis for dimension 4. These operators (called covariants of conformal change) can be constructed on a Riemannian \(S^ 4\) and a Lorentzian \(S^ 1\times S^ 3\) but there are problems with generalizing them to covariants on general manifolds. Dimension 4 is exceptional since there a non-existence theorem holds: there is no properly fourth-order covariant of conformal change acting on 1-forms in Riemannian or pseudo-Riemannian 4-manifolds.
Reviewer: L.Sokolowski

MSC:
53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B50 Applications of local differential geometry to the sciences