\(\operatorname{Spin}^c\)-structures and Dirac operators on contact manifolds

DOI10.1016/j.difgeo.2005.01.003zbMath1074.53042OpenAlexW1979036284WikidataQ115357987 ScholiaQ115357987MaRDI QIDQ1775938

Robert Petit

Publication date: 4 May 2005

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2005.01.003

zbMATH Keywords

Dirac operatorvanishing theoremsTanaka-Webster connectioncontact metric manifoldspin\(^c\)-structure

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Spin and Spin({}^c) geometry (53C27) Global Riemannian geometry, including pinching (53C20) Contact manifolds (general theory) (53D10) Almost complex manifolds (32Q60)

Related Items (17)

GEOMETRY OF SPIN ANDSPIN^cSTRUCTURES IN THE M-THEORY PARTITION FUNCTION ⋮ Twisted partially pure spinors ⋮ Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4 ⋮ SEIBERG-WITTEN-LIKE EQUATIONS ON THE STRICTLY PSEUDOCONVEX CR-3 MANIFOLDS ⋮ Seiberg-Witten Floer spectra and contact structures ⋮ Laplacians on smooth distributions ⋮ Spinorially twisted spin structures. III: CR structures ⋮ Adapted connections on metric contact manifolds ⋮ The Bochner-type formula and the first eigenvalue of the sub-Laplacian on a contact Riemannian manifold ⋮ Parallel spinors and basic holonomy in pseudo-Hermitian geometry ⋮ 5d Higgs branch localization, Seiberg-Witten equations and contact geometry ⋮ Dirac operators on the Fefferman spin spaces in almost CR-geometry ⋮ Adiabatic limits, vanishing theorems and the noncommutative residue ⋮ On the Yamabe problem on contact Riemannian manifolds ⋮ Invariant Dirac operators, harmonic spinors, and vanishing theorems in CR geometry ⋮ The first eigenvalue of the Kohn-Dirac operator on CR manifolds ⋮ Mok-Siu-Yeung type formulas on contact locally sub-symmetric spaces

Cites Work

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• Lorentzian twistor spinors and CR-geometry
• Geometric superrigidity
• Differential forms on contact manifolds
• Yang-Mills connections over compact strongly pseudoconvex CR manifolds
• Generic metrics and connections on spin- and \(\text{spin}^c\)-manifolds
• Seiberg-Witten monopoles on Seifert fibered spaces
• Sub-Riemannian limit of the differential form spectrum of contact manifolds
• Eigenvalue estimates for the Dirac operator depending on the Weyl tensor
• Harmonic maps and strictly pseudoconvex CR manifolds.
• Variational Problems on Contact Riemannian Manifolds
• On Pseudohermitian Immersions Between Strictly Pseudoconvex CR Manifolds
• On contact sub-riemannian symmetric spaces
• On vanishing theorems and rigidity of locally symmetric manifolds

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