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

JEFFREY S. CASE, A. Rod Gover

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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 algorithmboth 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.

Original languageEnglish (US)
Pages (from-to)565-618
Number of pages54
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Volume20
Issue number2
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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