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

Abstract

We study Kohn-Dirac operators $D_{\theta }$ on strictly pseudoconvex CR manifolds with ${\mathrm{spin}}^{\mathbb{C}}$ 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.

References in corpus (1)

• Kählerian Twistor Spinors