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Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study Kohn–Dirac operators $D_\theta$ on strictly pseudoconvex CR manifolds with ${\rm spin}^{\mathbb C}$ structure of weight $\ell\in{\mathbb Z}$. Certain components of $D_\theta$ are CR invariants. We also derive CR invariant twistor operators of weight $\ell$. 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.
Keywords: CR geometry, spin geometry, Kohn–Dirac operator, harmonic spinors, Kohn–Rossi cohomology, vanishing theorems. 
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     author = {Felipe Leitner},
     title = {Invariant {Dirac} {Operators,} {Harmonic} {Spinors,} and {Vanishing} {Theorems} in {CR} {Geometry}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a10/}
}
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Felipe Leitner. Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a10/

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