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arXiv · 2608.27569

Laplace and Dolbeault operators on Sasakian manifolds

Georges Habib·Ken Richardson·Robert Wolak
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Abstract

Sasakian manifolds, the odd-dimensional analogues of K\"ahler manifolds, carry two natural pairs of first-order Dolbeault-type operators on the full complex of differential forms, extending the Kohn--Rossi differentials. On such Sasaki manifolds, we establish K\"ahler-type identities for these operators, and relate the resulting Dolbeault Laplacians to the Hodge Laplacian. Unlike the K\"ahler case, where $\Delta=2\Delta_{\overline\partial}$, the relation has extra terms coming from the Reeb flow. Using these formulas and a Lefschetz decomposition, we derive lower and upper eigenvalue estimates for $\Delta$ on forms depending on the eigenvalues of the Lie derivative of the Reeb vector field.

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Georges Habib, Ken Richardson, Robert Wolak. 2026-08-27. Laplace and Dolbeault operators on Sasakian manifolds. https://arxiv.org/abs/2608.27569

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