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 |
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| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| 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| _version_ | 1862695251913736192 |
|---|---|
| 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.
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| first_indexed | 2026-03-18T05:46:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211177 |
| 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 |