K\"ahlerian Twistor Spinors

TL;DR

This paper explores K"ahlerian twistor spinors on K"ahler spin manifolds, providing a complete classification of compact cases with constant scalar curvature and linking their existence to Dirac operator spectra.

Contribution

It offers a comprehensive description of compact K"ahler manifolds admitting K"ahlerian twistor spinors and relates their existence to spectral bounds of the Dirac operator.

Findings

Complete classification of compact K"ahler manifolds with such spinors.

Connection established between spinor existence and Dirac spectrum.

Extension of twistor spinor theory to K"ahler geometry.

Abstract

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.