CR $Q$-curvature and CR pluriharmonic functions

TL;DR

This paper proves that on certain CR manifolds, the CR Q-curvature is orthogonal to CR pluriharmonic functions, providing a cohomological expression for their integral product, advancing understanding of CR geometric analysis.

Contribution

It establishes the orthogonality of CR Q-curvature to CR pluriharmonic functions and derives a cohomological formula for their integral product.

Findings

CR Q-curvature is orthogonal to CR pluriharmonic functions

Derived a cohomological expression for the integral of their product

Results apply to closed strictly pseudoconvex CR manifolds of dimension at least five

Abstract

In this paper, we show that the CR $Q$-curvature is orthogonal to the space of CR pluriharmonic functions on any closed strictly pseudoconvex CR manifold of dimension at least five. To this end, we obtain a cohomological expression of the integral of the product of the CR $Q$-curvature and a CR pluriharmonic function.