2017/09/23 by Case, Jeffrey S., Gover, A. Rod · 1 citation
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1709.08057
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.