Harmonic forms and the Rumin complex on Sasakian manifolds
Differential Geometry
2022-11-28 v2 Complex Variables
Symplectic Geometry
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.
Cite
@article{arxiv.2204.03446,
title = {Harmonic forms and the Rumin complex on Sasakian manifolds},
author = {Akira Kitaoka},
journal= {arXiv preprint arXiv:2204.03446},
year = {2022}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:2009.03276