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

Lichnerowicz, André

C. R. Acad. Sci., Paris, Sér. I 309, No. 1, 41-45 (1989).

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.)

Keywords:

spin manifolds; Killing spinor

Citations:

Zbl 0676.53053