Twistor Spinors with Zero on Lorentzian 5-Space

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Twistor Spinors with Zero on Lorentzian 5-space

Abstract. We present in this paper a C-metric on an open neighbourhood of the origin in R5. The metric is of Lorentzian signature (1, 4) and admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin. The construction is based on the Eguchi-Hanson metric with parallel spinors on Riemannia...

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About Twistor Spinors with Zero in Lorentzian Geometry

We describe the local conformal geometry of a Lorentzian spin manifold (M, g) admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ has isolated zeros then the metric g is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and g is locally conformally equivalent to a Brinkmann metric. Our ...

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Lorentzian twistor spinors and CR-geometry

In the present paper we study a relation between the Lorentzian twistor equation and CR-geometry. Besides the Dirac operator there is a second important conformally covariant differential operator acting on the spinor fields Γ(S) of a smooth semiRiemannian spin manifold (M,g) of dimension n and index k, the so-called twistor operator D. The twistor operator is defined as the composition of the ...

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ژورنال

عنوان ژورنال: Communications in Mathematical Physics

سال: 2007

ISSN: 0010-3616,1432-0916

DOI: 10.1007/s00220-007-0326-z