Skew Killing spinors. (English) Zbl 1246.53069
Authors’ abstract: We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.
Reviewer’s remark: Section 2 is called “Basics about spinors”, but two important definitions – ‘Clifford multiplication’ , ‘natural Hermitian product’ – are not made available to the reader.
Reviewer’s remark: Section 2 is called “Basics about spinors”, but two important definitions – ‘Clifford multiplication’ , ‘natural Hermitian product’ – are not made available to the reader.
Reviewer: Peter Kraut (Erlabrunn)
MSC:
| 53C27 | Spin and Spin\({}^c\) geometry |
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