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

• Jeffrey S. Case ^[1] ; A. Rod Gover ^[2]
  1. [1] Pennsylvania State University

     Pennsylvania State University

     Borough of State College, Estados Unidos

     
  2. [2] University of Auckland

     University of Auckland

     Nueva Zelanda

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 2, 2020, págs. 565-618
• Idioma: inglés
• Enlaces
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• Resumen

  • We establish an algorithm which computes formulae for the CR GJMS operators, the P0-operator, and the Q0-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 P0-operator, and shows that the Q0-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 P0-operator and Q0-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.