Harmonic forms and the Rumin complex on Sasakian manifolds

Abstract

We show that the kernel of the Rumin Laplacian agrees with that of the Hodge-de Rham Laplacian on compact Sasakian manifolds. As a corollary, we obtain another proof of primitiveness of harmonic forms. Moreover, the space of harmonic forms coincides with the sub-Riemann limit of Hodge-de Rham Laplacian when its limit converges. Finally, we express the analytic torsion function associated with the Rumin complex in terms of the Reeb vector field.