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 |
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| 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| 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.
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| ISSN: | 1815-0659 |