Les spineurs-twisteurs sur une variété spinorielle compacte. (Twistor-spinors on a compact spin manifold). (French) Zbl 0641.53014

Let (W,g) be an oriented compact spin manifold of dimension \(n\geq 3\), having a positive definite metric g. The author studies a first order differential operator D on (W,g) introduced by him previously [ibid. 304, 227-231 (1987; Zbl 0605.53030); Lett. Math. Phys. 13, 331-344 (1987; Zbl 0624.53034)] and establishes its conformal covariance. This result is then applied to twistor-spinors and harmonic spinors. By applying the Yamabe- Schoen theorem [cf. R. Schoen, J. Differ. Geom. 20, 479-496 (1984; Zbl 0576.53028)] it is proven that if the space \({\mathcal K}\) of twistor- spinors of (W,g) is not reduced to zero, then there exists a conformal change of the metric g which yields a manifold having non-zero Killing spinors. Finally the author presents an interpretation of the dimension of \({\mathcal K}\) involving these spaces of Killing spinors.
Reviewer: J.D.Zund


53C27 Spin and Spin\({}^c\) geometry
53C80 Applications of global differential geometry to the sciences