We construct the CR invariant canonical contact form $can\left(J\right)$ on scalar positive spherical CR manifold $(M,J)$, which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold $\Omega \left(\Gamma \right)/\Gamma$, where $\Gamma$ is a convex cocompact subgroup of ${Aut}_{CR}{\text{S}}^{2n+1}=PU(n+1,1)$ and $\Omega \left(\Gamma \right)$ is the discontinuity domain of $\Gamma$. This contact form can be used to prove that $\Omega \left(\Gamma \right)/\Gamma$ is scalar positive (respectively, scalar negative, or scalar vanishing) if and...

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields.Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators.Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0,1)$ vector fields satisfies...