Abstract
We prove that for non-linear L = L(R), G = dL/dR ≠ 0 the Lagrangians L and ^L(^R) with ^L = 2R/G3 - 3L/G4, ^gij = G2 gij and ^R = 3R/G2 - 4L/G3 give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator □ - R/6 is conformally invariant.
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