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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 339–357
DOI: 10.4171/ZAA/954

Published online: 2000-06-30

Some New Conformal Covariants

V. Wünsch[1]

(1) Friedrich-Schiller-Universität Jena, Germany

By means of a certain conformal covariant differentiation process explicit formulae are derived for
(i) a conformally invariant generalized Bach tensor in dimension 6
(ii) conformally invariant differential operators acting on weighted functions, especially one with leading term $?^4$
(iii) conformal covariants on symmetric, trace-free p-tensor bundles, especially one with leading term $?^2$
(iv) conformal covariants on differential forms.
Furthermore, theorems for uniqueness, existence and non-existence of conformal covariants, in particular in dimension 4, are given.

Keywords: Conformal transformation, conformally invariant tensor, conformally invariant differential operator, Bach tensor, conformal covariant derivative

Wünsch V.: Some New Conformal Covariants. Z. Anal. Anwend. 19 (2000), 339-357. doi: 10.4171/ZAA/954