Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus
By A. Gover, Lawrence J. Peterson. 2002
216 citations recorded by the source corpus.
Abstract: We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c126dd753c0c14a3d2c6e46bc50f88d076ab8d24
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Citations in the corpus
- Conformally invariant powers of the Laplacian — A complete nonexistence theorem (2004, unknown): “However if g is conformally (cid:13)at, it turns out that L g is the unique conformally invariant operator between densities whose leading part is ( (cid:0) (cid:1)) k ; see e.g., Proposition 2.1 of [12] or [9].”
- Compactness of solutions to some geometric fourth-order equations (2004, background): “Finally, we also point out that the Paneitz operator and the Q-curvature (together with their higher-dimensional analogues, see [5], [6], [27], [29]) appear in the study of Moser-Trudinger type inequalities, log-determinant formulas and the compactification of locally conformally flat manifolds, see”
- Standard Tractors and the Conformal Ambient Metric Construction (2002, methodology): “Some of these ideas were sketched in [ 12 ] but here we generalise the setting considerably.”
- CR invariant powers of the sub-Laplacian (2003, unknown): “D G ] 9 J an 2”