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nearly Kähler structures; nearly parallel $\mathrm {G}_2$-structures

References:

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[3] Friedrich, Th., Kath I., Moroianu A., Semmelmann U.: **On nearly parallel $\mathrm{G}_2$-structures**. J. Geom. Phys. 23 (1997), 259–286. MR 1484591

[4] Gray A.: **Vector cross products on manifolds**. Trans. Amer. Math. Soc. 141 (1969), 465–504. MR 0243469 | Zbl 0182.24603

[5] Gray A.: **Six-dimensional almost complex manifolds defined by means of three-fold vector cross products**. Tohoku Math. J. II. Ser. 21 (1969), 614–620. MR 0261515 | Zbl 0192.59002

[6] Grunewald R.: **Six-dimensional Riemannian manifolds with a real Killing spinor**. Ann. Global Anal. Geom. 8 (1990), 43–59. MR 1075238 | Zbl 0704.53050