The P'-operator, the Q'-curvature, and the CR tractor calculus

We establish an algorithm which computes formulae for the CR GJMS operators, the P'-operator, and the Q'-curvature in terms of CR tractors. When applied to torsion-free pseudo-Einstein contact forms, this algorithm both gives an explicit factorisation of the CR GJMS operators and the P'-operator, and shows that the Q'-curvature is constant, with the constant explicitly given in terms of the Webster scalar curvature. We also use our algorithm to derive local formulae for the P'-operator and Q'-curvature of a five-dimensional pseudo-Einstein manifold. Comparison with Marugame’s formulation of the Burns-Epstein invariant as the integral of a pseudohermitian invariant yields new insights into the class of local pseudohermitian invariants for which the total integral is independent of the choice of pseudo-Einstein contact form.

This is the accepted manuscript version of the following article: Jeffrey S. Case and A. Rod Gover, “The P'-operator, the Q'-curvature, and the CR tractor calculus,” Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2020: Vol. XX, Issue 2, doi: https://doi.org/10.2422/2036-2145.201710_001.

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Work Title The P'-operator, the Q'-curvature, and the CR tractor calculus
Access
Open Access
Creators
  1. Jeffrey S. Case
  2. A. Rod Gover
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Scuola Normale Superiore - Edizioni della Normale
Publication Date May 19, 2020
Publisher Identifier (DOI)
  1. 10.2422/2036-2145.201710_001
Source
  1. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
Deposited May 09, 2022

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