Global secondary CR invariants in dimension five

TL;DR

This paper characterizes all global secondary CR invariants in five-dimensional CR manifolds, showing they are linear combinations of known curvature integrals and local invariants, advancing understanding of CR geometry.

Contribution

It provides a complete classification of global secondary CR invariants in dimension five, identifying their structure as linear combinations of specific curvature integrals.

Findings

Any global secondary CR invariant in dimension five is a linear combination of the total $Q'$-curvature, total $ ext{I}'$-curvature, and a local CR invariant.

The invariants are independent of the choice of pseudo-Einstein contact form.

The result advances the understanding of CR invariants in five-dimensional geometry.

Abstract

A global secondary CR invariant is defined as the integral of a pseudo-hermitian invariant which is independent of a choice of pseudo-Einstein contact form. We prove that any global secondary CR invariant on CR five-manifolds is a linear combination of the total $Q'$-curvature, the total $\mathcal{I}'$-curvature, and the integral of a local CR invariant.