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arXiv · 2204.03446

Harmonic forms and the Rumin complex on Sasakian manifolds

Akira Kitaoka
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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.

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BibTeXRIS

Akira Kitaoka. 2022-04-07. Harmonic forms and the Rumin complex on Sasakian manifolds. https://arxiv.org/abs/2204.03446

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