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\begin{align} L=R-4\dfrac{n-1}{n-2}\nabla^k\nabla_k \end{align} What is the formal name for $L$? I have seen it referred to as the conformal laplacian, however I thought I once read $L$ with a formal name in another article, possibly named after some else?

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  • $\begingroup$ I don't think I've seen any name other than "conformal Laplacian". Are you perhaps thinking of the Paneitz operator, the conformal analogue of $\Delta^2$? en.wikipedia.org/wiki/Paneitz_operator $\endgroup$ May 2, 2015 at 11:54
  • $\begingroup$ @Travis I honestly don't remember. I have a faint memory of Paneltz though. $\endgroup$ May 2, 2015 at 12:14

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In Lorentzian signature, the conformal Laplacian is also known as the conformal wave operator. In Riemannian signature, it is also known as the Yamabe operator. The reason for these names is mentioned on page 14 of Sean Curry & Rod Gover's conformal geometry notes.

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