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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author Leitner, Felipe
author_facet Leitner, Felipe
citation_txt Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry. Felipe Leitner. SIGMA 17 (2021), 011, 25 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2026-03-18T05:46:14Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-18T05:46:14Z
publishDate 2021
publisher Інститут математики НАН України
record_format dspace
spelling Leitner, Felipe
2025-12-25T13:23:24Z
2021
Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry. Felipe Leitner. SIGMA 17 (2021), 011, 25 pages
1815-0659
2020 Mathematics Subject Classification: 32V05; 53C27; 58J50; 32L20
arXiv:2102.02477
https://nasplib.isofts.kiev.ua/handle/123456789/211177
https://doi.org/10.3842/SIGMA.2021.011
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.
I would like to thank the referees for their helpful comments.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
Article
published earlier
spellingShingle Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
Leitner, Felipe
title Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
title_full Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
title_fullStr Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
title_full_unstemmed Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
title_short Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
title_sort invariant dirac operators, harmonic spinors, and vanishing theorems in cr geometry
url https://nasplib.isofts.kiev.ua/handle/123456789/211177
work_keys_str_mv AT leitnerfelipe invariantdiracoperatorsharmonicspinorsandvanishingtheoremsincrgeometry