Abstract
Using a link between Einstein-Sasakian structures and Killing spinors we prove a general construction principle of odd-dimensional Riemannian manifolds with real Killing spinors. In dimensionn=7 we classify all compact Riemannian manifolds with two or three Killing spinors. Finally we classify nonflat 7-dimensional Riemannian manifolds with parallel spinor fields.
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Communicated by L. Alvarez-Gaumé
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Friedrich, T., Kath, I. 7-Dimensional compact Riemannian manifolds with Killing spinors. Commun.Math. Phys. 133, 543–561 (1990). https://doi.org/10.1007/BF02097009
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DOI: https://doi.org/10.1007/BF02097009