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Sur les résultats de H. Baum et Th. Friedrich concernant les spineurs de Killing à valeur propre imaginaire. (On the results of H. Baum and Th. Friedrich concerning the Killing spinors with an imaginary eigenvalue). (French) Zbl 0676.53052

Summary: A study of spin manifolds is made admitting a spinor \(\psi\) \(\not\equiv 0\) such that \(\nabla \psi +(f/n)\gamma \psi =0,\) where f is a complex- valued function (special case of a spinor-twistor). From the results of H. Baum [ibid., 47-49 (see below)] and Th. Friedrich [On the conformal relation between twistors and Killing spinors (to appear)], we show that there is only one case where \(\psi\) is not a Killing spinor and we analyze this case. We give an example of a compact manifold for which this situation is realized.

MSC:

53C20 Global Riemannian geometry, including pinching
53C27 Spin and Spin\({}^c\) geometry
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)

Citations:

Zbl 0676.53053
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