Variétés riemanniennes compactes de dimension 7 admettant des spineurs de Killing. (7-dimensional compact Riemannian manifolds admitting Killing spinors). (French) Zbl 0659.53017

Friedrich, Thomas; Kath, Ines

C. R. Acad. Sci., Paris, Sér. I 307, No. 19, 967-969 (1988).

The authors give a construction and classification of 7-dimensional compact Riemannian manifolds admitting Killing spinors. Such manifolds are shown to be Einstein spaces having positive scalar curvature. Various topological properties of these manifolds are discussed, and the authors remark that their methods may be extended to include a classification involving two or three parallel spinor fields.

Reviewer: J.D.Zund

MSC:

53C27	Spin and Spin\({}^c\) geometry
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

spinor structure; construction; classification; Killing spinors; Einstein spaces