Some Remarks on the Total CR $Q$ and $Q^{\prime }$-Curvatures

Abstract

We prove that the total CR $Q$-curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the $P^{\prime }$-operator and the CR invariance of the total $Q^{\prime }$-curvature for any pseudo-Einstein manifold without the assumption that it bounds a Stein manifold.

References in corpus (3)

• Variation of total Q-prime curvature on CR manifolds
• The $P^{\prime }$-operator, the $Q^{\prime }$-curvature, and the CR tractor calculus
• Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles

Cited by in corpus (4)

• Ambient constructions for Sasakian $\eta$-Einstein manifolds
• CR $Q$-curvature and CR pluriharmonic functions
• Analysis of the critical CR GJMS operator
• Generalizations of the $Q$-prime curvature via renormalized characteristic forms