Some Further Properties of Kählerian Twistor Spinors

✍ Scribed by K.-D. Kirchberg

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 1021 KB
• Volume: 163
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19931630120

✦ Synopsis

Abstract

On a spin Kähler manifold M^2m^ a new first integral Q~Ψ~ of the Kählerian twistor equations is presented. If the scalar curvature has a critical point then Q~Ψ~ vanishes. In case M^2m^ is closed, this fact provides a simple geometrical obstruction for Kählerian twistor spinors and, consequently, some new vanishing theorems. Twistor spinors with Q~Ψ~ ≠ 0 are investigated. Some invariants of the corresponding space of twistor spinors are constructed if the other basic first integral C~Ψ~ does not vanish, too. Each twistor spinor Ψ with C~Ψ~ ≠ 0 and Q~Ψ~ ≠ 0 determines a foliation of M^2m^ whose leaves are totally geodesic immersed Kähler manifolds. It is shown that Kählerian twistor spinors of type (r, s) can be interpreted as the minima of a certain functional. Some properties of Kählerian twistor spinors of the exceptional type r = (m + 2)/2 are proved.