We prove a vanishing theorem for Spinq manifolds admitting S1 actions, generalizing those of Atiyah and Hirzebruch for Spin manifolds and Hattori for Spinc manifolds. We also prove a vanishing theorem for almost quaternionic manifolds with compatible circle actions. To cite this article: H. Herrera, R. Herrera, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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