Kählerian Twistor Spinors

Details Kählerian Twistor Spinors Kählerian Twistor Spinors

2008-12-17

arxiv.org/abs/0812.3315v2

Mathematics

Differential Geometry

shorter version; to appear in Math.Z

Scientific paper

10.1007/s00209-010-0668-7

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.

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