Some Q-curvature Operators on Five-Dimensional Pseudohermitian Manifolds

Abstract

We construct Q-curvature operators on d-closed (1, 1)-forms and on $$\overline{\partial }_b$$ -closed (0, 1)-forms on five-dimensional pseudohermitian manifolds. These closely related operators give rise to a new formula for the scalar Q-curvature. As applications, we give a cohomological characterization of CR five-manifolds which admit a Q-flat contact form, and we show that every closed, strictly pseudoconvex CR five-manifold with trivial first real Chern class admits a Q-flat contact form provided the Q-curvature operator on $$\overline{\partial }_b$$ -closed (0, 1)-forms is nonnegative.