Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry

We study Kohn-Dirac operators θ on strictly pseudoconvex CR manifolds with spinℂ structure of weight ℓ ∈ ℤ. Certain components of θ are CR invariants. We also derive CR invariant twistor operators of weight ℓ. Harmonic spinors correspond to cohomology classes of some twisted Kohn-Rossi complex. Appl...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2021
Main Author: Leitner, Felipe
Format: Article
Language:English
Published: Інститут математики НАН України 2021
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211177
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry. Felipe Leitner. SIGMA 17 (2021), 011, 25 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We study Kohn-Dirac operators θ on strictly pseudoconvex CR manifolds with spinℂ structure of weight ℓ ∈ ℤ. Certain components of θ are CR invariants. We also derive CR invariant twistor operators of weight ℓ. Harmonic spinors correspond to cohomology classes of some twisted Kohn-Rossi complex. Applying a Schrödinger-Lichnerowicz-type formula, we prove vanishing theorems for harmonic spinors and (twisted) Kohn-Rossi groups. We also derive obstructions to positive Webster curvature.
ISSN:1815-0659