PreprintarXiv licencearXiv
Laplace and Dolbeault operators on Sasakian manifolds
Abstract
Sasakian manifolds, the odd-dimensional analogues of Kähler 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 Kähler-type identities for these operators, and relate the resulting Dolbeault Laplacians to the Hodge Laplacian. Unlike the Kähler case, where Δ=2Δ∂̅, 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 Δ on forms depending on the eigenvalues of the Lie derivative of the Reeb vector field.
Related
- Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace–Beltrami Operators on Manifolds
- Hitchin sections on $3$-dimensional Sasakian manifolds
- Dolbeault cohomology of Endo-Pajitnov manifolds
- Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
- Characterization of Sasakian Manifolds by Curvature Conditions
BibTeX
@misc{habib2026laplace,
title = {{Laplace and Dolbeault operators on Sasakian manifolds}},
author = {Georges Habib and Ken Richardson and Robert Wolak},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27569},
eprint = {2608.27569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27569},
}
RIS
TY - UNPB
TI - Laplace and Dolbeault operators on Sasakian manifolds
AU - Georges Habib
AU - Ken Richardson
AU - Robert Wolak
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27569
UR - https://arxiv.org/abs/2608.27569
AB - Sasakian manifolds, the odd-dimensional analogues of Kähler 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 Kähler-type identities for these operators, and relate the resulting Dolbeault Laplacians to the Hodge Laplacian. Unlike the Kähler case, where Δ=2Δ_∂̅, 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 Δ on forms depending on the eigenvalues of the Lie derivative of the Reeb vector field.
ER -