Functional Determinant on Pseudo-Einstein 3-manifolds

Abstract

Given a three dimensional pseudo-Einstein CR manifold (M, T 1,0 M, θ), we establish an expression for the difference of determinants of the Paneitz type operators A θ , related to the problem of prescribing the Q ′ -curvature, under the conformal change θ → e w θ with w ∈ P the space of pluriharmonic functions. This generalizes the expression of the functional determinant in four dimensional Riemannian maniflolds established in [6].